iopscience.org/jphysa Journal of Physics A Mathematical and Theoretical

Highlights of 2011 Cover image: Artistic impression of nontrivial cycles and stabilizer code generators on a lattice from ‘Constructions and noise threshold of topological subsystem codes’ by M Suchara et al 2011 J. Phys. A: Math. Theor. 44 155301. Journal of Physics A: Mathematical and Theoretical

Dear colleagues, 2011 has been another successful year for Journal of Physics A: Mathematical and Theoretical. The journal continues to have a broad audience and readers can enjoy high-quality research across theoretical and mathematical physics. This collection of highlights displays some of the most highly rated articles published in the journal during 2011. All of these articles were chosen primarily for their high-quality science. This selection displays the broad scope of the journal and demonstrates that it is a meeting place for researchers to share mathematically rich work across different disciplines. In 2011 we began to publish Insights: these are online, author-written news items highlighting the key achievements of recent work published in the journal to readers who might not be specialists in the field. All papers in this collection that have an associated Insight article are clearly marked. IMPACT FACTOR Some of our best articles have been published as Fast Track Communications (FTCs). FTCs * are short articles presenting important new developments in mathematical and theoretical 1.564 physics. FTCs benefit from accelerated publication and our recommended reader service, * As listed in ISI®’s 2011 Science Citation Index Journal Citation Reports where we will notify researchers selected by the authors when the article is published. Each year we award up to three articles the Journal of Physics A Best Paper Prize to reward AVERAGE DOWNLOADS work that has excelled in novelty, achievement, potential impact and presentation. Details PER ARTICLE of the 2011 winners can be found in this brochure. Please contact the journal office to make your nominations for future awards. This collection also shows details of the topical reviews and special issues that we have 159 published throughout 2011. Topical reviews are commissioned by our Board Members to provide timely overviews of the current state of research in areas of great interest and ACCEPTANCE TIMES activity, while special issues are collections of articles focused on contemporary areas IN 2011 of research, with contributions from world-class authors, and guest-edited by leading researchers. 86 DAYS* 2012 will be another strong year for the journal, with four special issues planned on * median receipt to acceptance Coherent states: mathematical and physical aspects; Applications of zeta functions and other spectral functions in mathematics and physics: a special issue in honour of Stuart Dowker’s 75th birthday; Quantum physics with non-Hermitian operators; and Lattice models and integrability: a special issue in honour of F Y Wu. We hope that you enjoy this collection. We would like to thank all of our authors for choosing to submit high-quality work to the journal as well as our referees for providing constructive peer review and maintaining the quality standards of the journal. We look forward to working with you during 2012. Murray Batchelor Editor-in-Chief

Highlights of 2011 3 Journal of Physics A: Mathematical and Theoretical

Editorial Board

Editor-in-Chief M T Batchelor Australian National University, Canberra, Australia

Statistical Physics Editor Quantum Mechanics and Quantum Information Theory Editor M R Evans University of Edinburgh, UK V Scarani National University of Singapore, Singapore

Chaotic and Complex Systems Editor Field Theory and String Theory Editor A Pikovsky Universität Potsdam, Germany A Tseytlin Imperial College, London, UK

Mathematical Physics Editor Fluid and Plasma Theory Editor A Kuniba University of Tokyo, Japan G Falkovich Weizmann Institute of Science, Israel

Editorial Board A V Kitaev Steklov Mathematical Institute, St Petersburg, Russia N Beisert ETH, Zurich, Switzerland G Korchemsky Université de Paris-Sud, France E Ben-Naim Los Alamos National Laboratory, USA C Maes Katholieke Universiteit Leuven, Belgium M V Berry University of Bristol, UK S Majumdar Université de Paris-Sud, France J-S Caux Universiteit van Amsterdam, The Netherlands R Metzler University of Potsdam, Germany M-Y Choi Seoul National University, Korea J A Minahan Uppsala Universitet, Sweden S Coppersmith University of Wisconsin, Madison, USA S Nazarenko University of Warwick, UK B Derrida École Normale Supérieure, France A M Ozorio de Almeida Centro Brasileiro de Pesquisas Fisicas, Brazil D Dhar Tata Institute of Fundamental Research, India J H H Perk Oklahoma State University, Stillwater, USA P E Dorey University of Durham, UK A Pumir École Normale Supérieure de Lyon, France J Eisert University of Potsdam, Germany P Schmelcher Universität Hamburg, Germany E Elizalde CSIC, Barcelona, Spain P Sollich King's College London, UK P Fendley University of Virginia, USA R Tumulka Rutgers University, USA O Gühne Universität Siegen, Germany M Visser Victoria University of Wellington, Wellington, New Zealand U Günther Forschungszentrum Rossendorf, Dresden, Germany A Vulpiani Università di Roma ‘La Sapienza’, Italy D D Holm Imperial College London, UK and Los Alamos National Laboratory, Y Wang Chinese Academy of Sciences, Beijing, China USA P Wiegmann University of Chicago, USA M Horodecki Gdan´sk University, Poland H-Q Zhou Chongqing University, People’s Republic of China K Kajiwara Kyushu University, Japan

Please do not send any manuscripts directly to our Board Members. Articles should be submitted via our website or by e-mail to [email protected].

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4 Highlights of 2011 Journal of Physics A: Mathematical and Theoretical

Journal scope

ISSN 1751-8113 Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research Journal of Physics A on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.

Mathematical papers should be clearly motivated by actual or potential application to physical phenomena.

Volume 44 Number 50 16 December 2011 Research papers published in Journal of Physics A: Mathematical and Theoretical are categorized into one of six subject sections:

•statistical physics •chaotic and complex systems •mathematical physics •quantum mechanics and quantum information theory •field theory and string theory iopscience.org/jphysa •fluid and plasma theory

To be accepted for publication in the journal, papers must make significant, original and correct contributions to one or more of the topics within these sections.

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Highlights of 2011 5 Journal of Physics A: Mathematical and Theoretical

Contents

Statistical physics

Universal statistics and control of random transport processes 9 Iddo Eliazar and Joseph Klafter

Fermi edge resonances in non-equilibrium states of Fermi gases 9 E Bettelheim, Y Kaplan and P Wiegmann

Functional Bethe ansatz methods for the open XXX chain 9 Holger Frahm, Jan H Grelik, Alexander Seel and Tobias Wirth

An exact formula for the statistics of the current in the TASEP with open boundaries 9 Alexandre Lazarescu and Kirone Mallick

The grand canonical ABC model: a reflection asymmetric mean-field Potts model 10 J Barton, J L Lebowitz and E R Speer

Non-equilibrium 1D many-body problems and asymptotic properties of Toeplitz determinants 10 D B Gutman, Yuval Gefen and A D Mirlin

Residual mean first-passage time for jump processes: theory and applications to Lévy flights and fractional Brownian motion 10 V Tejedor, O Bénichou, Ralf Metzler and R Voituriez

Thermodynamics and spin-charge separation of one-dimensional strongly repulsive three-component fermions 11 Peng He, Jen Yee Lee, Xiwen Guan, Murray T Batchelor and Yupeng Wang

Diffusion with optimal resetting 11 Martin R Evans and Satya N Majumdar

Replica approach to the KPZ equation with the half Brownian motion initial condition 11 Takashi Imamura and Tomohiro Sasamoto

Chaotic and complex systems

Universal emergence of PageRank In 12 K M Frahm, B Georgeot and D L Shepelyansky

Optimum principle for a vehicular traffic network: minimum probability of congestion In 12 Boris S Kerner

Loschmidt echo in quantum maps: the elusive nature of the Lyapunov regime 12 Ignacio García-Mata and Diego A Wisniacki

Isochronal synchronization of time delay and delay-coupled chaotic systems In 13 J M V Grzybowski , E E N Macau and T Yoneyama

Time-dependent scattering theory for ODEs and applications to reaction dynamics 13 Daniel Blazevski and Rafael de la Llave

In Insight available

6 Highlights of 2011 Journal of Physics A: Mathematical and Theoretical

Mathematical physics

A compact hamiltonian with the same asymptotic mean spectral density as the Riemann zeros 14 M V Berry and J P Keating

On natural Poisson bivectors on the sphere 14 A V Tsiganov

A modular invariant bulk theory for the c=0 triplet model 14 Matthias R Gaberdiel, Ingo Runkel and Simon Wood

On sums of tensor and fusion multiplicities 14 Robert Coquereaux and Jean-Bernard Zuber

Highest weight Macdonald and Jack polynomials 15 Th Jolicoeur and J G Luque

Quantum loop subalgebra and eigenvectors of the superintegrable chiral Potts transfer matrices 15 Helen Au-Yang and Jacques H H Perk

Solvable vector nonlinear Riemann problems, exact implicit solutions of dispersionless PDEs and wave breaking 15 S V Manakov and P M Santini

The classical trigonometric r-matrix for the quantum-deformed Hubbard chain 16 Niklas Beisert

A nonseparable quantum superintegrable system in 2D real Euclidean space 16 Sarah Post and Pavel Winternitz

The Berry–Keating Hamiltonian and the local Riemann hypothesis 16 Mark Srednicki

Quantum mechanics and quantum information theory

Non-equilibrium steady states of quantum systems on star graphs 17 Mihail Mintchev

The quantum Arnold transformation 17 V Aldaya, F Cossío, J Guerrero and F F López-Ruiz

A note on the optimality of decomposable entanglement witnesses and completely entangled subspaces In 17 R Augusiak, J Tura and M Lewenstein

Complete characterization of extreme quantum observables in infinite dimensions 17 Juha-Pekka Pellonpää

Extremal correlations of the tripartite no-signaling polytope In 18 Stefano Pironio, Jean-Daniel Bancal and Valerio Scarani

Correlation-induced non-Abelian quantum holonomies 18 Markus Johansson, Marie Ericsson, Kuldip Singh, Erik Sjöqvist and Mark S Williamson

Physics within a quantum reference frame 18 Renato M Angelo, Nicolas Brunner, Sandu Popescu, Anthony J Short and Paul Skrzypczyk

In Insight available

Highlights of 2011 7 Journal of Physics A: Mathematical and Theoretical

Constructions and noise threshold of topological subsystem codes 19 Martin Suchara, Sergey Bravyi and Barbara Terhal

Simulating quantum dynamics on a quantum computer 19 Nathan Wiebe, Dominic W Berry, Peter Høyer and Barry C Sanders

Low-dimensional quite noisy bound entanglement with a cryptographic key 19 Łukasz Pankowski and Michał Horodecki

Field theory and string theory

Nonassociative gravity in string theory? 20 R Blumenhagen and E Plauschinn

Symmetries of noncommutative scalar field theory 20 Axel de Goursac and Jean-Christophe Wallet

Frame-like geometry of double field theory 20 Olaf Hohm and Seung Ki Kwak

Amplitudes at weak coupling as polytopes in AdS5 20 Lionel Mason and David Skinner

Complete conformal field theory solution of a chiral six-point correlation function 21 Jacob J H Simmons and Peter Kleban

Lifshitz formula for the Casimir force and the Gelfand–Yaglom theorem 21 C Ccapa Ttira, C D Fosco and F D Mazzitelli

On strong-coupling correlation functions of circular Wilson loops and local operators 21 Luis F Alday and Arkady A Tseytlin

W-algebras and surface operators in N=2 gauge theories 21 Niclas Wyllard

An action principle for Vasiliev’s four-dimensional higher spin gravity 22 Nicolas Boulanger and Per Sundell

N=2 S-duality via outer-automorphism twists 22 Yuji Tachikawa

Fluid and plasma theory

Lyapunov exponent for small particles in smooth one-dimensional flows 22 Michael Wilkinson

Landau damping: the mechanics model and its ultimate entropy gain 22 J H Hannay and Michel Kluge

Exploring Born–Infeld electrodynamics using plasmas 23 D A Burton, R M G M Trines, T J Walton and H Wen

Application of the multicomponent lattice Boltzmann simulation method to oil/water dispersions 23 M A Seaton, I Halliday and A J Masters

Differential geometric structures of stream functions: incompressible two-dimensional flow and curvatures 23 K Yamasaki, T Yajima and T Iwayama

Journal of Physics A invites you to submit your article online at authors.iop.org

8 Highlights of 2011 Journal of Physics A: Mathematical and Theoretical q Statistical physics Functional Bethe ansatz methods for the open XXX chain

Universal statistics and control of random Holger Frahm, Jan H Grelik, Alexander Seel and Tobias Wirth transport processes Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstr. 2, 30167 Hannover, Germany Iddo Eliazar1 and Joseph Klafter2 1 Department of Technology Management, Holon Institute of Technology, 2011 J. Phys. A: Math. Theor. 44 015001 PO Box 305, Holon 58102, Israel 2 School of Chemistry, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel We study the spectrum of the integrable open XXX Heisenberg spin chain subject to non-diagonal boundary magnetic fields. The spectral problem for

this model can be formulated in terms of functional equations obtained by 2011 J. Phys. A: Math. Theor. 44 222001 separation of variables or, equivalently, from the fusion of transfer matrices. Fast Track Communications For generic boundary conditions the eigenvalues cannot be obtained from the solution of finitely many algebraic Bethe equations. Based on careful finite size studies of the analytic properties of the underlying hierarchy A general model of random transport is considered: independent agents of transfer matrices we devise two approaches to analyze the functional are stochastically emitted into a space with general topology; the agents’ equations. First we introduce a truncation method leading to Bethe-type motion in space is governed by a general random transport mechanism; the equations determining the energy spectrum of the spin chain. In a second agents are detected only when in a target zone which is an arbitrary subset approach, the hierarchy of functional equations is mapped to an infinite of space. We explore emission intensities which render the agents’ ‘target- system of nonlinear integral equations of TBA type. The two schemes have zone statistics’ universal, i.e. invariant with respect to the underlying spatial complementary ranges of applicability and facilitate an efficient numerical topology and transport mechanism. The results established determine how analysis for a wide range of boundary parameters. Some data are presented to universally control the target-zone statistics via the emission intensity, on the finite-size corrections to the energy of the state which evolves into the and show that the resulting universal statistics are governed by power laws. antiferromagnetic ground state in the limit of parallel boundary fields.

Root distributions for the B-state at α ± = 11i/3 and ch φ = 11. Zeros belonging to fixed lattice sizes L = 1–9 Fermi edge resonances in non-equilibrium are each connected by a dashed line as a guidance states of Fermi gases for the eyes. The roots on the imaginary axis forming an asymptotic lattice of half- E Bettelheim1, Y Kaplan1 and P Wiegmann2 integers are not displayed. 1 Racah Institute of Physics, Hebrew University, Jerusalem, Israel 2 The James Franck Institute, University of Chicago, Chicago, IL, USA

2011 J. Phys. A: Math. Theor. 44 282001

Fast Track Communications An exact formula for the statistics of the We formulate the problem of the Fermi edge singularity in non-equilibrium states of a Fermi gas as a matrix Riemann–Hilbert problem with an current in the TASEP with open boundaries integrable kernel. This formulation is the most suitable for studying the singular behavior at each edge of non-equilibrium Fermi states by means of Alexandre Lazarescu and Kirone Mallick the method of steepest descent, and also reveals the integrable structure of Institut de Physique Théorique, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France the problem. We supplement this result by extending the familiar approach to the problem of the Fermi edge singularity via the bosonic representation 2011 J. Phys. A: Math. Theor. 44 315001 of the electronic operators to non-equilibrium settings. It provides a compact way to extract the leading asymptotes. We study the totally asymmetric exclusion process on a finite one-dimensional lattice with open boundaries, i.e. in contact with two reservoirs at different potentials. The total (time-integrated) current through the system is a random variable that scales linearly with time in the long-time limit. We conjecture a parametric representation for the generating function of the cumulants of the current, which is related to the large deviation function by Laplace transform. This formula is valid for all system sizes and for all values of the boundary coupling parameters.

Occupation of electronic states in a structured Fermi sea. Illustration of the TASEP with open boundaries on a finite lattice with L sites.

Highlights of 2011 9 Journal of Physics A: Mathematical and Theoretical

and establish interrelations between all these problems. The results can The grand canonical ABC model: a reflection be expressed in terms of Fredholm determinants of the Toeplitz type. We analyze the long time asymptotics of such determinants, using Szego´´ and asymmetric mean-field Potts model Fisher–Hartwig theorems. Our analysis yields dephasing rates as well as power-law scaling behavior, with exponents depending not only on the J Barton1, J L Lebowitz1,2 and E R Speer2 interaction strength but also on the non-equilibrium state of the system. 1 Department of Physics, Rutgers University, Piscataway, NJ 08854-8019, USA Schematic results for TDOS in a LL with not- 2 Department of Mathematics, Rutgers University, Piscataway, NJ 08854-8019, USA too-strong interaction and with multiple-step distributions. The distributions of electrons from both reservoirs are assumed to be 2011 J. Phys. A: Math. Theor. 44 065005 equal and of the type shown in figure 1(A) (upper panel) or figure 1(B) (lower panel).

The exponents γi characterizing ZBA at We investigate the phase diagram of a three-component system of particles multiple edges are indicated. All singularities are broadened by the non-equilibrium on a one-dimensional filled lattice, or equivalently of a one-dimensional dephasing rate 1/2τφ. three-state Potts model, with reflection asymmetric mean-field interactions. The three types of particles are designated as A, B and C. The system is described by a grand canonical ensemble with temperature T and chemical potentials TλA, TλB and TλC. We find that for λA = λB = λC the system undergoes a phase transition from a uniform density to a continuum of ˆ –1 phases at a critical temperature Tc=(2π /√3) . For other values of the chemical potentials the system has a unique equilibrium state. As is the case for the canonical ensemble for this ABC model, the grand canonical ensemble is the stationary measure satisfying detailed balance for a natural ˆ dynamics. We note that Tc=3Tc, where Tc is the critical temperature for a similar transition in the canonical ensemble at fixed equal densities rA = rB

= rC = 1/3.

Curves Γβ in the rA–rB plane along which F(r) achieves its minimum value, Residual mean first-passage time for jump for β1 = 3.75, β2 = 4.25 and β3 = 6.05 (βt = 2π/√3 b 3.63). c processes: theory and applications to Lévy flights and fractional Brownian motion

V Tejedor1,2, O Bénichou1, Ralf Metzler2,3 and R Voituriez1 1 Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), Université Pierre et Marie Curie, 4 Place Jussieu, 75255 Paris Cedex, France 2 Physics Department, Technical University of Munich, James Franck Strasse, 85747 Garching, Germany 3 Physics Department, Tampere University of Technology, FI-33101 Tampere, Finland

2011 J. Phys. A: Math. Theor. 44 255003 Non-equilibrium 1D many-body problems and asymptotic properties of Toeplitz We derive a functional equation for the mean first-passage time (MFPT) of a generic self-similar Markovian continuous process to a target in a determinants one-dimensional domain and obtain its exact solution. We show that the obtained expression of the MFPT for continuous processes is actually 1 2 3,4,5 D B Gutman , Yuval Gefen and A D Mirlin different from the large system size limit of the MFPT for discrete jump 1 Department of Physics, Bar Ilan University, Ramat Gan 52900, Israel processes allowing leapovers. In the case considered here, the asymptotic 2 Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot MFPT admits non-vanishing corrections, which we call residual MFPT. The 76100, Israel case of Lévy flights with diverging variance of jump lengths is investigated 3 Institut für Nanotechnologie, Karlsruhe Institute of Technology, 76021 Karlsruhe, in detail, in particular, with respect to the associated leapover behavior. Germany We also show numerically that our results apply with good accuracy to 4 Institut für Theorie der kondensierten Materie, Karlsruhe Institute of Technology, fractional Brownian motion, despite its non-Markovian nature. 76128 Karlsruhe, Germany MFPT for a Lévy flight, for several 5 Petersburg Nuclear Physics Institute, 188300 St. Petersburg, Russia sizes of the 1D lattice (200, 400, 800, 1600, 3200 and 6400 sites, from black (bottom) to light gray 2011 J. Phys. A: Math. Theor. 44 165003 (top) as the size grows) compared to the theoretical expression (16) (magenta dotted line, the A constant being given by equation (23)), and Non-equilibrium bosonization technique facilitates the solution of a number for dw = 1.25. of important many-body problems out of equilibrium, including the Fermi-edge singularity, the tunneling spectroscopy and full counting statistics of interacting fermions forming a Luttinger liquid. We generalize the method to non-equilibrium hard-core bosons (Tonks–Girardeau gas)

10 Highlights of 2011 Journal of Physics A: Mathematical and Theoretical

can reduce the mean time to absorption provided that the initial position Thermodynamics and spin-charge separation is sufficiently far from the target. We address the problem of optimal resetting, that is, minimizing the mean time to absorption for a given target of one-dimensional strongly repulsive three- distribution. For an exponentially decaying target distribution centred at the component fermions origin we show that a transition in the optimal resetting distribution occurs as the target distribution narrows.

Peng He1,2, Jen Yee Lee2, Xiwen Guan2, Murray T Batchelor2,3 and Yupeng Wang1 Schematic spacetime 1 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, trajectory of a one- dimensional Brownian Chinese Academy of Sciences, Beijing 100190, People’s Republic of China motion that starts at x0 and 2 Department of Theoretical Physics, Research School of Physics and Engineering, resets stochastically to its initial position x at rate r. Australian National University, Canberra ACT 0200, Australia 0 3 Mathematical Sciences Institute, Australian National University, Canberra ACT 0200, Australia

2011 J. Phys. A: Math. Theor. 44 405005

The low-temperature thermodynamics of one-dimensional strongly repulsive SU(3) fermions in the presence of a magnetic field is investigated via the Yang–Yang thermodynamic Bethe ansatz method. The analytical free energy and magnetic properties of the model at low temperatures in a weak magnetic field are derived via the Wiener–Hopf method. It is shown Replica approach to the KPZ equation with that the low-energy physics can be described by spin-charge separated conformal field theories of an effective Tomonaga–Luttinger liquid and an the half Brownian motion initial condition antiferromagnetic SU(3) Heisenberg spin chain. Beyond the Tomonaga– Luttinger liquid regime, the equation of state is given in terms of the polylog Takashi Imamura1 and Tomohiro Sasamoto2 function for a weak external field. The results obtained are essential for 1 Research Center for Advanced Science and Technology, The University of Tokyo, further study of quantum criticality in strongly repulsive three-component Japan fermions. 2 Department of Mathematics and Informatics, Chiba University, Japan The plot shows C –T curves V for external magnetic field H = 0.001, chemical 2011 J. Phys. A: Math. Theor. 44 385001 potential µ = 6 and coupling constant c = 30. We consider the one-dimensional Kardar–Parisi–Zhang (KPZ) equation with the half Brownian motion initial condition, studied previously through the weakly asymmetric simple exclusion process. We employ the replica Bethe ansatz and show that the generating function of the exponential moments of the height is expressed as a Fredholm determinant. From this, the height distribution and its asymptotics are studied. Furthermore, using the replica method we also discuss the multi-point height distribution. We find that some good properties of the deformed Airy functions play an important role in the analysis. Half Brownian motion initial condition. Diffusion with optimal resetting

Martin R Evans1,2 and Satya N Majumdar2,3 1 SUPA, School of Physics and Astronomy, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, UK 2 Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel 3 University Paris-Sud, CNRS, LPTMS, UMR 8626, Orsay F-01405, France

2011 J. Phys. A: Math. Theor. 44 435001 PEER REVIEW TIMES IN 2011 First decision times* We consider the mean time to absorption by an absorbing target of a diffusive particle with the addition of a process whereby the particle is reset to its initial position with rate r. We consider several generalizations of the model of Evans and Majumdar (2011 Phys. Rev. Lett. 106 160601): (i) a space-dependent resetting rate r(x); (ii) resetting to a random 34 DAYS position z drawn from a resetting distribution P(z); and (iii) a spatial distribution for the absorbing target PT(x). As an example of (i) we show *median receipt to first decision time that the introduction of a non-resetting window around the initial position

Highlights of 2011 11 Journal of Physics A: Mathematical and Theoretical

simulations with a stochastic three-phase traffic flow model, we show that q Chaotic and complex systems in comparison to the well-known Wardrops principles, the application of the BM principle permits considerably greater network inflow rates at which no traffic breakdown occurs and, therefore, free flow remains in the whole Insight network. Universal emergence of available (B) Probability of traffic breakdown PFS PageRank at a single on-ramp bottleneck as a function of the flow rate downstream of the bottleneck for on-ramp inflow rates K M Frahm, B Georgeot and D L Shepelyansky −1 qon = 1000 vehicles h . Laboratoire de Physique Théorique du CNRS, IRSAMC, Université de Toulouse, UPS, 31062 Toulouse, France

2011 J. Phys. A: Math. Theor. 44 465101

The PageRank algorithm enables us to rank the nodes of a network through a specific eigenvector of the Google matrix, using a damping parameter α e ]0, 1[. Using extensive numerical simulations of large web networks, Loschmidt echo in quantum maps: the with a special accent on British University networks, we determine numerically and analytically the universal features of the PageRank vector elusive nature of the Lyapunov regime at its emergence when α → 1. The whole network can be divided into a core part and a group of invariant subspaces. For α → 1, PageRank converges Ignacio García-Mata1,2,3 and Diego A Wisniacki4 to a universal power-law distribution on the invariant subspaces whose 1 Departamento de Física, Lab. TANDAR–CNEA, Buenos Aires, Argentina size distribution also follows a universal power law. The convergence of 2 Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), CONICET–UNMdP, PageRank at α → 1 is controlled by eigenvalues of the core part of the Funes 3350, B7602AYL Mar del Plata, Argentina Google matrix, which are extremely close to unity, leading to large relaxation 3 Consejo Nacional de Investigaciones Científicas y Tecnológicas (CONICET), times as, for example, in spin glasses. Argentina 4 Departamento de Física, FCEyN UBA, and IFIBA, CONICET, Pabellón 1 Ciudad Universitaria, C1428EGA Buenos Aires, Argentina

2011 J. Phys. A: Math. Theor. 44 315101

The Loschmidt echo (LE) is a measure of the stability and reversibility of quantum evolution under perturbations of the Hamiltonian. One of the expected and most relevant characteristics of this quantity for chaotic systems is an exponential decay with a perturbation-independent decay rate given by the classical Lyapunov exponent. However, a non-uniform decay—instead of the Lyapunov regime—has been reported in several Left panels (right panels) correspond to Cambridge 2006 (Oxford 2006). Subspace eigenvalues systems. In this work, we find an analytical semiclassical expression for the of the matrix S (blue dots or crosses) and core space eigenvalues (red dots) in the λ–plane (green averaged fidelity amplitude that can be directly related to the anomalous— curve shows unit circle); here N = 48 239 (30 579). There are 1543 (1889) invariant subspaces, s unexpected—behaviour of the LE. with maximal dimension 4656 (1545) and the sum of all subspace dimensions is Ns = 48 239

(30 579). The core space eigenvalues are obtained from the AM applied to the block Scc with Arnoldi dimension 20 000 and are numerically accurate for |λ|H 0.7.

Insight Optimum principle for a available vehicular traffic network: minimum probability of congestion

Boris S Kerner Daimler AG, GR/PTF, HPC: G021, 71059 Sindelfingen, Germany

2011 J. Phys. A: Math. Theor. 44 092001

Fast Track Communications

– Decay rate ΓLE as a function of the rescaled perturbation Σ/h for the quantum perturbed cat map We introduce an optimum principle for a vehicular traffic network with road with N = 218 and for different values of a and b (different values of λ, indicated by the dashed bottlenecks. This network breakdown minimization (BM) principle states lines). (4) a = b = 1, λ ≈ 0.96; (L) a = b = 2, λ ≈ 1.76; (3) a = b = 4, λ ≈ 2.887; (X) a = b = 6, λ ≈ 3.637; (o) a = b = 20, λ ≈ 5.996. The perturbation is f (q) (equation (27)). The solid line that the network optimum is reached when link flow rates are assigned in 1 corresponds to ΓDR and the dash-dot line σSC . Averages were done over 2048 initial states. the network in such a way that the probability for spontaneous occurrence AFA LDOS of traffic breakdown in at least one of the network bottlenecks during a given observation time reaches the minimum possible value. Based on numerical

12 Highlights of 2011 Journal of Physics A: Mathematical and Theoretical

Insight Time-dependent scattering theory for ODEs Isochronal synchronization of available time delay and delay-coupled and applications to reaction dynamics chaotic systems Daniel Blazevski and Rafael de la Llave Department of Mathematics, University of Texas, 1 University Station C1200, Austin, J M V Grzybowski1, E E N Macau2 and T Yoneyama3 TX 78712, USA 1 Instituto Tecnológico de Aeronáutica, ITA, Praça Marechal Eduardo Gomes, 50,

Vila das Acácias, São José dos Campos, SP, Brazil, CEP 12.228-900 2011 J. Phys. A: Math. Theor. 44 195101 2 Instituto Nacional de Pesquisas Espaciais, INPE, PO Box 515, São José dos Campos, SP, Brazil, CEP 12.227-010 3 Instituto Tecnológico de Aeronáutica, ITA, Praça Marechal Eduardo Gomes, 50, We develop a time-dependent scattering theory for general vector fields Vila das Acácias, São José dos Campos, SP, Brazil, CEP 12.228-900 in Euclidean space. We give conditions that ensure that the wave maps exist, are smooth, invertible, and depend smoothly on parameters. We then 2011 J. Phys. A: Math. Theor. 44 175103 discuss the intertwining relations and how they can be used to compute stable/unstable manifolds for time-dependent normally hyperbolic invariant manifolds. The theory is particularly effective for Hamiltonian This paper studies the problem of isochronal synchronization of time-delay mechanics. We also give perturbative calculations of the scattering map chaotic systems featuring also coupling delay. Based on the Lyapunov– that are analogous to Fermi's golden rule in quantum mechanics. We apply Krasovskii stability theory, sufficient conditions are derived for the stability this theory to a problem in transition state theory concerning the exposure of isochronal synchronization between a pair of identical chaotic systems. of molecules to a laser pulse for a short time. We present a method to Such criteria permit the proper design of stable proportional linear feedback compute invariant manifolds for the laser-driven Henon–Heilies system and controller, more specifically, the design of adequate proportional feedback give perturbative calculations of the change in the branching ratio. gain matrices. The proposed criteria are suited to systems with (i) intrinsic Pictorial description of the wave and delay, (ii) coupling delay or (iii) both. Numerical simulations of the scattering maps. For a given point x0 let synchronization of delay-coupled systems are presented as examples of the x± := X t0. Then V t (x ) converges in the future 0 ± t0 0 (resp. past) to U t (x+) (resp. U –t (x–)) and application of the criteria. t0 0 t0 0 – the scattering map takes x0 as an input and + outputs x0.

Synchronization error for the Lorenz hyperchaotic system, τ = 0.2.

Insights Visit our homepage to read what our authors have to say about their work

Highlights of 2011 13 Journal of Physics A: Mathematical and Theoretical q Mathematical physics A modular invariant bulk theory for the c=0 triplet model

A compact hamiltonian with the same Matthias R Gaberdiel1, Ingo Runkel2 and Simon Wood1 asymptotic mean spectral density as the 1 Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland 2 Department Mathematik, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Riemann zeros Germany

M V Berry1 and J P Keating2 2011 J. Phys. A: Math. Theor. 44 015204 1 H H Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, UK 2 School of Mathematics, University of Bristol, Bristol BS8 1TW, UK W A proposal for the bulk space of the logarithmic 2,3-triplet model at 2011 J. Phys. A: Math. Theor. 44 285203 central charge zero is made. The construction is based on the idea that one may reconstruct the bulk theory of a rational conformal field theory from its boundary theory. The resulting bulk space is a quotient of the direct sum of For the classical hamiltonian (x + 1/x)(p + 1/p), with position x and projective representations, which is isomorphic, as a vector space, to the conjugate momentum p, all orbits are bounded. After a symmetrization, the direct sum of tensor products of the irreducible representations with their corresponding quantum integral equation possesses a family of self-adjoint projective covers. As a consistency check of our analysis, we show that extensions: compact operators on the entire positive x axis, labelled by the partition function of the bulk theory is modular invariant, and that the an angle α specifying the boundary condition at the origin, with a discrete boundary state analysis is compatible with the proposed annulus partition spectrum of real energies E. On the cylinder {−∞ < E < ∞, 0 G α < 2π}, functions of this model. there is a single eigencurve in the form of a helix winding clockwise. The rise between successive windings gets sharper as the scaled Planck's constant decreases. This behaviour can be understood semiclassically. The first two terms of the asymptotic eigenvalue density are the same as those for the density of heights of the Riemann zeros. On sums of tensor and fusion multiplicities

(a) 3D plot of hamiltonian H(x, p) (1.3), with 1 2 quadrants labelled Q. (b) Shaded contour Robert Coquereaux and Jean-Bernard Zuber plot of H(x, p) in first quadrant, with light 1 Centre de Physique Théorique (CPT), CNRS UMR 6207, Luminy, Marseille, France representing high and dark low. 2 Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589 and Université Pierre et Marie Curie-Paris 6, 4 Place Jussieu, 75252 Paris Cedex 05, France

2011 J. Phys. A: Math. Theor. 44 295208

The total multiplicity in the decomposition into irreducibles of the tensor product λ ⊗ μ of two irreducible representations of a simple Lie algebra ν - ν is invariant under conjugation of one of them: Σν N λ μ = Σν Nλ μ. This also applies to the fusion multiplicities of affine algebras in conformal WZW theories. In that context, the statement is equivalent to a property

of the modular S-matrix, namely Σ(κ) := Σ λSλκ = 0 if κ is a complex representation. Curiously, this vanishing Σ(κ) also holds when κ is a quaternionic representation. We provide proofs of all these statements. These proofs rely on a case-by-case analysis, maybe overlooking some hidden symmetry principle. We also give various illustrations of these properties in the contexts of boundary conformal field theories, integrable quantum field theories and topological field theories.

On natural Poisson bivectors on the sphere

A V Tsiganov St. Petersburg State University, St. Petersburg, Russia

2011 J. Phys. A: Math. Theor. 44 105203

The tensor product graph Nf for the subgroup Σ(1080). We discuss the concept of natural Poisson bivectors, which allows us to consider the overwhelming majority of known integrable systems on the sphere in the framework of bi-Hamiltonian geometry.

14 Highlights of 2011 Journal of Physics A: Mathematical and Theoretical

Highest weight Macdonald and Jack Solvable vector nonlinear Riemann polynomials problems, exact implicit solutions of dispersionless PDEs and wave breaking Th Jolicoeur1 and J G Luque2 1 LPTMS, CNRS et Université Paris-Sud, 91405 Orsay, France S V Manakov1 and P M Santini2 2 Laboratoire LITIS, EA 4108, Université de Rouen, Avenue de l’Université, 1 Landau Institute for Theoretical Physics, Moscow, Russia BP 8 76801 Saint-Étienne-du-Rouvray Cedex, France 2 Dipartimento di Fisica, Università di Roma ‘La Sapienza’, and Istituto Nazionale di

Fisica Nucleare, Sezione di Roma 1, Piazz.le Aldo Moro 2, I-00185 Roma, Italy 2011 J. Phys. A: Math. Theor. 44 055204

2011 J. Phys. A: Math. Theor. 44 345203 Fractional quantum Hall states of particles in the lowest Landau levels are described by multivariate polynomials. The incompressible liquid states when described on a sphere are fully invariant under the rotation group. We have recently solved the inverse spectral problem for integrable Excited quasiparticle/quasihole states are members of multiplets under the partial differential equations (PDEs) in arbitrary dimensions arising as rotation group and generically there is a nontrivial highest weight member commutation of multidimensional vector fields depending on a spectral of the multiplet from which all states can be constructed. Some of the trial parameter λ. The associated inverse problem, in particular, can be states proposed in the literature belong to classical families of symmetric formulated as a nonlinear Riemann–Hilbert (NRH) problem on a given polynomials. In this paper we study Macdonald and Jack polynomials contour of the complex λ plane. The most distinguished examples that are highest weight states. For Macdonald polynomials, it is a of integrable PDEs of this type, like the dispersionless Kadomtsev– (q, t)-deformation of the raising angular momentum operator that defines Petviashivili (dKP), the heavenly and the two-dimensional dispersionless the highest weight condition. By specialization of the parameters we obtain Toda equations, are real PDEs associated with Hamiltonian vector fields. a classification of the highest weight Jack polynomials. Our results are valid The corresponding NRH data satisfy suitable reality and symplectic in the case of staircase and rectangular partition indexing the polynomials. constraints. In this paper, generalizing the examples of solvable NRH problems illustrated in Manakov and Santini (2009 J. Phys. A: Math. Theor. 42 095203; 2008 J. Phys. A: Math. Theor. 41 055204; 2009 J. Phys. A: Math. Theor. 42 404013), we present a general procedure to construct solvable NRH problems for integrable real PDEs associated with Hamiltonian vector fields, allowing one to construct exact implicit solutions Quantum loop subalgebra and eigenvectors of such PDEs parametrized by an arbitrary number of real functions of a of the superintegrable chiral Potts transfer single variable. Then, we illustrate this theory on few distinguished examples for the dKP and heavenly equations. For the dKP case, we characterize a matrices class of similarity solutions, of solutions constant on their parabolic wave front and breaking simultaneously on it, of localized solutions whose Helen Au-Yang1,2 and Jacques H H Perk1,2 breaking point travels with constant speed along the wave front, and of 1 Department of Physics, Oklahoma State University, 145 Physical Sciences, localized solutions breaking in a point of the (x, y) plane. For the heavenly Stillwater, OK 74078-3072, USA equation, we characterize two classes of symmetry reductions. 2 Centre for Mathematics and its Applications & Department of Theoretical Physics, Australian National University, Canberra, ACT 2600, Australia The saddle wave front described by (114), before breaking, for 2011 J. Phys. A: Math. Theor. 44 025205 n = 4, a = 0.3, F(ζ) = 0.2e− ζ 2 and

t = tb − 1, where

tb = 25e/8. It has been shown in earlier works that for Q = 0 and L a multiple of N, the ground state sector eigenspace of the superintegrable τ2(tq) model is highly degenerate and is generated by a quantum loop algebra L(sl2). Furthermore, this loop algebra can be decomposed into r = (N − 1)L/N simple sl2 algebras. For Q ≠ 0, we shall show here that the corresponding eigenspace of τ2(tq) is still highly degenerate, but splits into two spaces, each containing 2r − 1 independent eigenvectors. The generators for the sl2 subalgebras, and also for the quantum loop subalgebra, are given generalizing those in the Q = 0 case. However, the Serre relations for the generators of the loop subalgebra are only proven for some states, tested on small systems and conjectured otherwise. Assuming their validity we construct the eigenvectors of the Q ≠ 0 ground state sectors for the transfer matrix of the superintegrable chiral Potts model.

Highlights of 2011 15 Journal of Physics A: Mathematical and Theoretical

The classical trigonometric r-matrix for the The Berry–Keating Hamiltonian and the local quantum-deformed Hubbard chain Riemann hypothesis

Niklas Beisert Mark Srednicki Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, Department of Physics, University of California, Santa Barbara, CA 93106, USA 14476 Potsdam, Germany 2011 J. Phys. A: Math. Theor. 44 305202 2011 J. Phys. A: Math. Theor. 44 265202

The local Riemann hypothesis states that the zeros of the Mellin transform The one-dimensional Hubbard model is an exceptional integrable spin of a harmonic-oscillator eigenfunction (on a real or p-adic configuration chain which is apparently based on a deformation of the Yangian for the space) have a real part 1/2. For the real case, we show that the imaginary superalgebra gl(2|2). Here we investigate the quantum deformation of parts of these zeros are the eigenvalues of the Berry–Keating Hamiltonian ˆ the Hubbard model in the classical limit. This leads to a novel classical HBK = (ˆx pˆ + ˆpˆ)/2x projected onto the subspace of oscillator eigenfunctions r-matrix of trigonometric kind. We derive the corresponding one-parameter of a lower level. This gives a spectral proof of the local Riemann hypothesis family of Lie bialgebras as a deformation of the affine gl(2|2) Kac–Moody for the reals, in the spirit of the Hilbert–Pólya conjecture. The p-adic case is superalgebra. In particular, we discuss the affine extension as well as also discussed. discrete symmetries, and we scan for simpler limiting cases, such as the rational r-matrix for the undeformed Hubbard model.

Journal of Physics A: Mathematical and Theoretical 2011 topical reviews

On the uncertainty in the regularized solution Daniel Keren and Ido Nissenboim

The compactified complex plane for z, x or y, respectively. The points corresponding to 2011 J. Phys. A: Math. Theor. 44 023001 & * z± = 0, ∞ are marked by &. The self-dual points corresponding to z± are marked by *. The spheres are divided into one, two or four regions which are identified by a twist. T-systems and Y-systems in integrable systems Atsuo Kuniba, Tomoki Nakanishi and Junji Suzuki 2011 J. Phys. A: Math. Theor. 44 103001

Disordered topological insulators: a non-commutative geometry A nonseparable quantum superintegrable perspective system in 2D real Euclidean space Emil Prodan 2011 J. Phys. A: Math. Theor. 44 113001 Tutorial on scale and conformal symmetries in diverse dimensions Sarah Post1 and Pavel Winternitz1,2 R Jackiw and S-Y Pi 2011 J. Phys. A: Math. Theor. 44 223001

1 Centre de recherches mathématiques, Université de Montréal, C.P. 6128 succ. Yangians, S-matrices and AdS/CFT Centre-Ville, Montréal (QC) H3C 3J7, Canada Alessandro Torrielli 2011 J. Phys. A: Math. Theor. 44 263001 2 Département de mathématiques et de statistique, Université de Montréal, C.P. 6128 succ. Centre-Ville, Montréal (QC) H3C 3J7, Canada Scalar field quantization without divergences in all spacetime dimensions 2011 J. Phys. A: Math. Theor. 44 162001 John R Klauder 2011 J. Phys. A: Math. Theor. 44 273001

RD Fast Track Communications Notes on Yang–Mills–Higgs monopoles and dyons on , and Chern–Simons–Higgs solitons on RD–2: dimensional reduction of In this paper, we derive a nonseparable quantum superintegrable system in Chern–Pontryagin densities 2D real Euclidean space. The Hamiltonian admits no second-order integrals D H Tchrakian 2011 J. Phys. A: Math. Theor. 44 343001 of motion but does admit an integral of third-order and an integral of fourth- Discrete quantum mechanics order. We also obtain a classical superintegrable system with the same Satoru Odake and Ryu Sasaki 2011 J. Phys. A: Math. Theor. 44 353001 properties. The quantm system differs from the classical one by corrections proportional to h- 2. Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories Marcos Mariño 2011 J. Phys. A: Math. Theor. 44 463001

Unconventional phase transitions in a constrained single polymer chain L I Klushin and A M Skvortsov 2011 J. Phys. A: Math. Theor. 44 473001

The effective temperature Leticia F Cugliandolo 2011 J. Phys. A: Math. Theor. 44 483001

16 Highlights of 2011 Journal of Physics A: Mathematical and Theoretical

q Quantum mechanics and quantum Insight A note on the optimality of available information theory decomposable entanglement witnesses and completely entangled Non-equilibrium steady states of quantum subspaces systems on star graphs R Augusiak1, J Tura2 and M Lewenstein1,3,4

1 Mihail Mintchev ICFO–Institut de Ciències Fotòniques, Parc Mediterrani de la Tecnologia, 08860 Castelldefels, Spain Istituto Nazionale di Fisica Nucleare and Dipartimento di Fisica, Universitá di Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy 2 Centre de Formació Interdisciplinària Superior, Universitat Politècnica de Catalunya, Pau Gargallo 5, 08028 Barcelona, Spain

2011 J. Phys. A: Math. Theor. 44 415201 3 ICREA–Institució Catalana de Recerca i Estudis Avançats, Lluis Companys 23, 08010 Barcelona, Spain 4 Kavli Institute for Theoretical Physics, University of California, Santa Barbara, Non-equilibrium steady states of quantum fields on star graphs are explicitly CA 93106-4030, USA constructed. These states are parametrized by the temperature and the chemical potential, associated with each edge of the graph. Time reversal 2011 J. Phys. A: Math. Theor. 44 212001 invariance is spontaneously broken. We study in this general framework the transport properties of the Schrödinger and the Dirac systems on a star Fast Track Communications graph, modeling a quantum wire junction. The interaction, which drives the system away from equilibrium, is localized in the vertex of the graph. Entanglement witnesses (EWs) constitute one of the most important All point-like vertex interactions, giving rise to self-adjoint Hamiltonians entanglement detectors in quantum systems. Nevertheless, their complete possibly involving the minimal coupling to a static electromagnetic field in characterization, in particular with respect to the notion of optimality, the ambient space, are considered. In this context, we compute the exact is still missing, even in the decomposable case. Here we show that for electric steady current and the non-equilibrium charge density. We also any qubit–qunit decomposable EW (DEW) W, the three statements are investigate the heat transport and derive the Casimir energy density away equivalent: (i) the set of product vectors obeying 〈e, f|W|e, f 〉 = 0 spans from equilibrium. The appearance of Friedel-type oscillations of the charge the corresponding Hilbert space, (ii) W is optimal, and (iii) W = QΓ, with and energy densities along the edges of the graph is established. We focus Q denoting a positive operator supported on a completely entangled finally on the noise power and discuss the non-trivial impact of the point-like subspace (CES) and Γ standing for the partial transposition. While interactions on the noise. implications (i) (ii) and (ii) (iii) are known, here we prove that (iii) implies (i). This is a consequence of a more general fact saying that product vectors orthogonal to any CES in C2 ⊗ Cn span after partial conjugation the whole space. On the other hand, already in the case of the C3 ⊗ C3 Hilbert space, there exist DEWs for which (iii) does not imply (i). Consequently, either (i) does not imply (ii) or (ii) does not imply (iii), and the above transparent characterization, obeyed by qubit–qunit DEWs, does not hold in general.

Contour plots of the noise P11 in the plane (β1, β2 ), (μ1,μ2 ) and (η1, η2 ), respectively. Complete characterization of extreme The quantum Arnold transformation quantum observables in infinite dimensions Juha-Pekka Pellonpää V Aldaya1, F Cossío1, J Guerrero1,2 and F F López-Ruiz1 Turku Centre for Quantum Physics, Department of Physics and Astronomy, University 1 Instituto de Astrofísica de Andalucía, CSIC, Apartado Postal 3004, 18080 Granada, of Turku, FI-20014 Turku, Finland Spain 2 Departamento de Matemática Aplicada, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spain 2011 J. Phys. A: Math. Theor. 44 085304

2011 J. Phys. A: Math. Theor. 44 065302 We give a complete characterization for extreme quantum observables, i.e. for normalized positive operator valued measures (POVMs) which are Using a quantum version of the Arnold transformation of classical extremals in the convex set of all POVMs. The characterization is valid mechanics, all quantum dynamical systems whose classical equations both in discrete and continuous cases, and also in the case of an of motion are non-homogeneous linear second-order ordinary differential infinite-dimensional Hilbert space. We show that sharp POVMs are equations, including systems with friction linear in velocity, can be related pre-processing clean, i.e. they cannot be irreversibly connected to other to the quantum free-particle dynamical system. This transformation POVMs via quantum channels. provides a basic (Heisenberg–Weyl) algebra of quantum operators, along with well-defined Hermitian operators which can be chosen as evolution-like observables and complete the entire Schrödinger algebra. It also proves to be very helpful in performing certain computations quickly, to obtain, for example, wavefunctions and closed analytic expressions for time-evolution operators.

Highlights of 2011 17 Journal of Physics A: Mathematical and Theoretical

Insight Extremal correlations of the available Physics within a quantum reference frame tripartite no-signaling polytope Renato M Angelo1,2, Nicolas Brunner2, Sandu Popescu2, Anthony J Short3 and Paul Skrzypczyk2 Stefano Pironio1, Jean-Daniel Bancal2 and Valerio Scarani3 1 Federal University of Parana, PO Box 19044, 81531-990, Curitiba, PR, Brazil 1 Laboratoire d’Information Quantique, Université Libre de Bruxelles, 2 H H Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, 1050 Brussels, Belgium BS8 1TL, UK 2 Group of Applied Physics, University of Geneva, Switzerland 3 DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, 3 Centre for Quantum Technologies and Department of Physics, National University CB3 0WA, UK of Singapore, Singapore 117543

2011 J. Phys. A: Math. Theor. 44 145304 2011 J. Phys. A: Math. Theor. 44 065303

We investigate the physics of quantum reference frames. Specifically, The no-signaling polytope associated with a Bell scenario with three parties, we study several simple scenarios involving a small number of quantum two inputs, and two outputs, is found to have 53 856 extremal points, particles, whereby we promote one of these particles to the role of a belonging to 46 inequivalent classes. We provide a classification of these quantum observer and ask what is the description of the rest of the system, points according to various definitions of multipartite nonlocality and briefly as seen by this observer? We highlight the interesting aspects of such discuss other issues such as the interconversion between extremal points questions by presenting a number of apparent paradoxes. By unravelling seen as a resource and the relation of the extremal points to Bell-type these paradoxes, we obtain a better understanding of the physics of inequalities. quantum reference frames.

Correlation-induced non-Abelian quantum holonomies

Markus Johansson1, Marie Ericsson1, Kuldip Singh2, Erik Sjöqvist1,2 and Mark S Williamson2,3 1 Department of Quantum Chemistry, Uppsala University, Box 518, Se-751 20 Uppsala, Sweden At T = 0, a quantum rocket is prepared in a well-localized state, whose centre of mass is depicted 2 Centre for Quantum Technologies, National University of Singapore, 3 Science here by the narrow central (red) wavepacket. Inside the rocket is a particle in superposition, Drive 2, 117543 Singapore, Singapore depicted here by the two outlying (blue) wavepackets, initially located at a distance L from

3 the centre of the rocket, with momentum p towards the centre. At a time T = mpL/p when the Erwin Schrödinger International Institute for Mathematical Physics, wavepackets interfere, either (a) the centre of mass is sufficiently localized to resolve the fringes Boltzmanngasse 9, 1090 Wien, Austria or (b) the centre of mass is too uncertain to resolve them.

2011 J. Phys. A: Math. Theor. 44 145301

In the context of two-particle interferometry, we construct a parallel transport condition that is based on the maximization of coincidence intensity with respect to local unitary operations on one of the subsystems. The dependence on correlation is investigated and it is found that the holonomy group is generally non-Abelian, but Abelian for uncorrelated systems. It is found that our framework contains the Lévay geometric phase (2004 J. Phys. A: Math. Gen. 37 1821) in the case of two-qubit systems undergoing local SU(2) evolutions. Iterative procedure in the first, second and (n + 1)st step.

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18 Highlights of 2011 Journal of Physics A: Mathematical and Theoretical

and accounts for all computational resources. We explicitly determine the Constructions and noise threshold of number of bits of output that this oracle needs to provide, and show how to efficiently perform the required 1-sparse unitary operations using these bits. topological subsystem codes We also account for discretization error in the time, as well as accounting for Hamiltonians that are a sum of terms that are sparse in different bases. Martin Suchara1, Sergey Bravyi2 and Barbara Terhal2 1 Princeton University, Princeton, NJ 08544, USA 2 IBM Watson Research Center, Yorktown Heights, NY 10598, USA

2011 J. Phys. A: Math. Theor. 44 155301

Topological subsystem codes proposed recently by Bombin are quantum error-correcting codes defined on a two-dimensional grid of qubits that This circuit simulates exp(−iHµ, j (tp)δtp) for the one-sparse Hamiltonian Hµ, j, given an input state of the form of the left-hand side of (66). Here the variable φ = Arg([H (t )] ) and permit reliable quantum information storage with a constant error threshold. µ, j p mx,Mx α = 2|[H (t )] |Δt . Here we also use rectangles to represent R rotations by a fixed angle, These codes require only the measurement of two-qubit nearest-neighbor µ, j p mx,Mx p z triangles represent Rx rotations and the pentagon represents a Ry rotation. These rotations can be operators for error correction. In this paper, we demonstrate that topological enacted by querying the oracle QMatrixVal and performing controlled rotations on the output. subsystem codes (TSCs) can be viewed as generalizations of Kitaev’s honeycomb model to 3-valent hypergraphs. This new connection provides a systematic way of constructing TSCs and analyzing their properties. We also derive a necessary and sufficient condition under which a syndrome Low-dimensional quite noisy bound measurement in a subsystem code can be reduced to measurements of the gauge group generators. Furthermore, we propose and implement some entanglement with a cryptographic key candidate decoding algorithms for one particular TSC assuming perfect 1,2 2 error correction. Our Monte Carlo simulations indicate that this code, which Łukasz Pankowski and Michał Horodecki we call the five-square code, has a threshold against depolarizing noise of 1 Institute of Informatics, University of Gdan´sk, Gdan´sk, Poland at least 2%. 2 Institute of Theoretical Physics and Astrophysics, University of Gdan´sk, Gdan´sk, Poland Basis cycles X1, X2 ∈ Z L ( so) corresponding to homologically non-trivial 2011 J. Phys. A: Math. Theor. 44 035301 horizontal loops on the lattice.

We provide a class of bound entangled states that have a positive distillable secure key rate. The smallest state of this kind is 4 ⊗ 4. Our class is a generalization of the class presented in Horodecki et al (2008 IEEE Trans. Inf. Theory 54 2621–5). It is much wider, containing, in particular, states from the boundary of PPT entangled states (all of the states in the previous class were of this kind) and also states inside the set of PPT entangled states, even approaching the separable states. This generalization comes at a price: for the wider class, a positive key rate requires, in general, apart from the one-way Devetak–Winter protocol (used in the previous case) also the recurrence preprocessing and thus is effectively a two-way protocol. We Simulating quantum dynamics on a quantum also analyze the amount of noise that can be admixtured to the states of our class without losing the key distillability property which may be crucial for computer experimental realization. The wider class contains key-distillable states with higher entropy (up to 3.524, as opposed to 2.564 for the previous class). 1 2 1,3 1,4 Nathan Wiebe , Dominic W Berry , Peter Høyer and Barry C Sanders A class of key-distillable PPT entangled 1 Institute for Quantum Information Science, University of Calgary, Alberta T2N 1N4, states: (a) the solid line from u˜ on the Canada boundary of the PPT entangled states (inclusive) to the boundary of the set of 2 Institute for Quantum Computing, University of Waterloo, Ontario N2 L 3G1, Canada u separable states, arbitrary close to sep; (b) 3 Department of Computer Science, University of Calgary, Alberta T2N 1N4, Canada the arc of PPT-invariant states starting in u˜ u and approaching arbitrary close to ˜max. 4 Department of Physics and Astronomy, University of Calgary, Alberta T2N 1N4, Canada

2011 J. Phys. A: Math. Theor. 44 445308

We explicitly show how to simulate time-dependent sparse Hamiltonian evolution on a quantum computer, with complexity that is close to linear in the evolution time. The complexity also depends on the magnitude of the derivatives of the Hamiltonian. We propose a range of techniques to simulate Hamiltonians with badly behaved derivatives. These include using adaptive time steps, adapting the order of the integrators, and omitting regions about discontinuities. The complexity of the algorithm is quantified by calls to an oracle, which yields information about the Hamiltonian,

Highlights of 2011 19 Journal of Physics A: Mathematical and Theoretical q Field theory and string theory Frame-like geometry of double field theory

Olaf Hohm and Seung Ki Kwak Nonassociative gravity in string theory? Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA R Blumenhagen1,3 and E Plauschinn2,3 1 Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, 2011 J. Phys. A: Math. Theor. 44 085404 80805 München, Germany 2 Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht, The Netherlands We relate two formulations of the recently constructed double field theory 3 Kavli Institute for Theoretical Physics, Kohn Hall, UCSB, Santa Barbara, CA 93106, to a frame-like geometrical formalism developed by Siegel. A self-contained USA presentation of this formalism is given, including a discussion of the constraints and its solutions, and of the resulting Riemann tensor, Ricci

tensor and curvature scalar. This curvature scalar can be used to define an 2011 J. Phys. A: Math. Theor. 44 015401 action, and it is shown that this action is equivalent to that of double field theory. In an on-shell conformal field theory approach, we find indications of a three-bracket structure for target space coordinates in general closed string backgrounds. This generalizes the appearance of noncommutative Amplitudes at weak coupling as polytopes in gauge theories for open strings in two-form backgrounds to a putative noncommutative/nonassociative gravity theory for closed strings probing AdS5 curved backgrounds with non-vanishing three-form flux. Several aspects and consequences of the three-bracket structure are discussed and a new Lionel Mason1 and David Skinner2 type of generalized uncertainty principle is proposed. 1 The Mathematical Institute, 24–29 St. Giles’, Oxford, OX1 3LB, UK 2 Behavior of the three-point function (47) Perimeter Institute for Theoretical Physics, 31 Caroline St, Waterloo, ON, N2L 2Y5, 123 for f = √2, k = 1, z3 = 0. Canada

2011 J. Phys. A: Math. Theor. 44 135401

We show that one-loop scalar box functions can be interpreted as volumes

of geodesic tetrahedra embedded in a copy of AdS5 that has dual conformal spacetime as boundary. When the tetrahedron is space-like, it lies in a

totally geodesic hyperbolic three-space inside AdS5, with its four vertices on the boundary. It is a classical result that the volume of such a tetrahedron is given by the Bloch–Wigner dilogarithm. We show that this agrees with the standard physics formulae for such box functions. The combinations of box functions that arise in the n-particle one-loop MHV amplitude in N=4 super Yang–Mills correspond to the volume of a three-dimensional polytope Symmetries of noncommutative Insight available without boundary, all of whose vertices are attached to a null polygon scalar field theory (which in other formulations is interpreted as a Wilson loop) at infinity. The 3-mass box integral has an entire edge Axel de Goursac1 and Jean-Christophe Wallet2 along the boundary at infinity, so its volume diverges. This edge lies along a null geodesic 1 Département de Mathématiques et Physique, Université Catholique de Louvain, (shown in blue) and the quadric X · X = 0 is Chemin du Cyclotron, 2, 1348 Louvain-la Neuve, Belgium ruled by these null lines. 2 Laboratoire de Physique Théorique, Bât. 210, Université Paris XI, F-91405 Orsay Cedex, France

2011 J. Phys. A: Math. Theor. 44 055401

We investigate symmetries of the scalar field theory with a harmonic term on the Moyal space with the Euclidean scalar product and general symplectic form. The classical action is invariant under the orthogonal group if this group acts also on the symplectic structure. We find that the invariance under the orthogonal group can also be restored at the quantum level by restricting the symplectic structures to a particular orbit. ACCEPTANCE RATE IN 2011 33%

20 Highlights of 2011 Journal of Physics A: Mathematical and Theoretical

Complete conformal field theory solution of a On strong-coupling correlation functions of chiral six-point correlation function circular Wilson loops and local operators

Jacob J H Simmons1,2 and Peter Kleban3 Luis F Alday1 and Arkady A Tseytlin2,3,4 1 Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, UK 1 Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK 2 James Franck Institute, 929 E 57th Street, Chicago, IL 60637, USA 2 Blackett Laboratory, Imperial College, London SW7 2AZ, UK 3 LASST and Department of Physics & Astronomy, University of Maine, Orono, 3 Kavli Institute for Theoretical Physics, University of California, Santa Barbara, ME 04469, USA CA 93106, USA 4 Also at Lebedev Institute, Moscow 2011 J. Phys. A: Math. Theor. 44 315403 2011 J. Phys. A: Math. Theor. 44 395401

Using conformal field theory, we perform a complete analysis of the chiral six-point correlation function C(z)=〈φ1,2φ1,2Φ1/2,0(z,z¯ )φ1,2φ1,2〉, with the four Motivated by the problem of understanding 3-point correlation functions

φ1,2 operators at the corners of an arbitrary rectangle, and the point of gauge-invariant operators in N=4 super Yang–Mills theory we consider z = x + iy in the interior. We calculate this for arbitrary central charge correlators involving Wilson loops and a ‘light’ operator with fixed quantum (equivalently, SLE parameter κ > 0). C is of physical interest because numbers. At leading order in the strong-coupling expansion such correlators for percolation (κ = 6) and many other two-dimensional critical points, it are given by the ‘light’ vertex operator evaluated on a semiclassical string specifies the density at z of critical clusters conditioned to touch either or world surface ending on the corresponding loops at the boundary of both vertical ends of the rectangle, with these ends ‘wired’, i.e. constrained 5 AdS5 × S . We study in detail the example of a correlator of two concentric to be in a single cluster, and the horizontal ends free. The correlation circular Wilson loops and a dilaton vertex operator. The resulting expression function may be written as the product of an algebraic prefactor f and a is given by an integral of combinations of elliptic functions and can conformal block G, where f = f(x, y, m), with m a cross-ratio specified by the be computed analytically in some special limits. We also consider a corners (m determines the aspect ratio of the rectangle). By appropriate generalization of the minimal surface ending on two circles to the case of choice of f and using coordinates that respect the symmetry of the problem, non-zero angular momentum J in S5 and discuss a special limit when one of the conformal block G is found to be independent of either y or x, and given the Wilson loops is effectively replaced by a ‘heavy’ operator with charge J. by an Appell function.

Lifshitz formula for the Casimir force and the Gelfand–Yaglom theorem

C Ccapa Ttira1, C D Fosco2,3 and F D Mazzitelli3,4 The two different solutions approach each other as the corresponding two values of p get closer 1 Instituto de Fisica – UFRJ, CP 68528, 21941-972 Rio de Janeiro, RJ, Brazil to p0. 2 Instituto Balseiro, Universidad Nacional de Cuyo, R8402AGP Bariloche, Argentina 3 Centro Atómico Bariloche, Comisión Nacional de Energía Atómica, R8402AGP Bariloche, Argentina 4 Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de W-algebras and surface operators in N=2 Buenos Aires, Ciudad Universitaria, Pabellón 1, 1428 Buenos Aires, Argentina gauge theories

2011 J. Phys. A: Math. Theor. 44 465403 Niclas Wyllard

We provide a quantum field theory derivation of the Lifshitz formula for the 2011 J. Phys. A: Math. Theor. 44 155401 Casimir force due to a fluctuating real scalar field in d + 1 dimensions. The field is coupled to two imperfect, thick, plane mirrors, which are modeled by W background potentials localized on their positions. The derivation proceeds A general class of -algebras can be constructed from the affine sl(N) from the calculation of the vacuum energy in the Euclidean version of the algebra by (quantum) Drinfeld–Sokolov reduction and are classified by N system, reducing the problem to the evaluation of a functional determinant. partitions of N. Surface operators in an =2 SU(N) 4D gauge theory are The latter is written, via Gelfand–Yaglom's formula, in terms of functions also classified by partitions of N. We argue that instanton partition functions N depending on the structure of the potential describing each mirror; those of =2 gauge theories in the presence of a surface operator can also W functions encode the properties which are relevant to the Casimir force and be computed from the corresponding -algebra. We test this proposal by analysing the Polyakov–Bershadsky W (2) algebra obtaining results are the reflection coefficients evaluated at imaginary frequencies. 3 that are in agreement with the known partition functions for SU(3) gauge The potential V(x ), using a typical d theories with a so-called simple surface operator. As a byproduct, our profile for the mirrors. W (2) W proposal implies relations between 3 and 3 algebras.

Highlights of 2011 21 Journal of Physics A: Mathematical and Theoretical

An action principle for Vasiliev’s q Fluid and plasma theory four-dimensional higher spin gravity Lyapunov exponent for small particles in Nicolas Boulanger1 and Per Sundell2 Service de Mécanique et Gravitation, Université de Mons—UMONS, 20 Place du Parc, smooth one-dimensional flows B-7000 Mons, Belgium 1 F.R.S.-FNRS Associate Researcher Michael Wilkinson 2 F.R.S.-FNRS Researcher with an Ulysse Incentive Grant for Mobility in Scientific Department of Mathematics and Statistics, The Open University, Milton Keynes Research MK7 6AA, UK

2011 J. Phys. A: Math. Theor. 44 495402 2011 J. Phys. A: Math. Theor. 44 045502

We provide Vasiliev’s fully nonlinear equations of motion for bosonic higher This paper discusses the Lyapunov exponent λ for small particles in a spin gauge fields in four spacetime dimensions with an action principle. spatially and temporally smooth flow in one dimension. The Lyapunov We first extend Vasiliev’s original system with differential forms in degrees exponent is obtained as a series expansion in the Stokes number, St, higher than 1. We then derive the resulting duality-extended equations of which is a dimensionless measure of the importance of inertial effects. The motion from a variational principle based on a generalized Hamiltonian approach described here can be extended to calculations of the Lyapunov sigma-model action. The generalized Hamiltonian contains two types of exponents and of the correlation dimension for inertial particles in higher interaction freedoms: one, a set of functions that appears in the Q-structure dimensions. It is shown that there is a correction to this theory which arises of the generalized curvatures of the odd forms in the duality-extended because the particles do not sample the velocity field ergodically. Using this system; and the other, a set depending on the Lagrange multipliers, non-ergodic correction, it is found that (contrary to expectations) the encoding a generalized Poisson structure, i.e. a set of polyvector fields of first-order term in the expansion of λ does not vanish. rank 2 or higher in target space. We find that at least one of the two sets of interaction-freedom functions must be linear in order to ensure gauge invariance. We discuss consistent truncations to the minimal type A and B models (with only even spins), spectral flows on-shell and provide boundary Landau damping: the mechanics model and conditions on fields and gauge parameters that are compatible with the its ultimate entropy gain variational principle and that make the duality-extended system equivalent, on-shell, to Vasiliev’s original system. J H Hannay and Michel Kluge H.H.Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK

N=2 S-duality via outer-automorphism 2011 J. Phys. A: Math. Theor. 44 055501 twists Classical mechanics has only been invoked to account for Landau damping Yuji Tachikawa in a rather half-hearted way, alongside plasma perturbation theory. In School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540, USA particular this invocation is essential for the study of the saturation, or post-linear (or ‘nonlinear’) regime of the damping initiated by Dawson and 2011 J. Phys. A: Math. Theor. 44 182001 O’Neill. By embracing mechanics wholeheartedly here, with its attendant phase space, one can access results, old and new, cleanly and directly, Fast Track Communications and with one fewer numerical integration for the post-linear regime. By using a summation technique familiar in semiclassical quantum mechanics Compactification of 6D N=(2,0) theory of type G on a punctured Riemann (Poisson summation), the one remaining numerical integration can surface has been effectively used to understand S-dualities of 4D N=2 be much improved in accuracy. Also accessible from mechanics is the theories. We can further introduce branch cuts on the Riemann surface ultimate entropy gain. Though zero for any finite time (in the absence of across which the worldvolume fields are transformed by the discrete coarse graining), the entropy gain is ultimately non-zero (at infinite time the symmetries associated with those of the Dynkin diagram of type G. This required coarse graining is zero). It is calculated analytically by using the allows us to generate more S-dualities, and in particular to reproduce a appropriate asymptotics, hitherto not fully exploited. couple of S-dual pairs found previously by Argyres and Wittig. In Landau damping a particle moves in a sinusoidal potential well, so the phase space energy contours are those of a pendulum with a lemon shaped ‘seperatrix’. The inside of this represents trapping (oscillatory motion), and the outside represents one-way motion (rightwards above, and leftwards below). The initial (a) This effectively represents a hyper in the bifundamental representation of SO(2N − 1) × probability distribution is also shown by USp(2N − 1). (b) Combining with (a) of figure 2, we get superconformal SO(2N − 1) theory. shading. It has straight contours, being a (Gaussian) function of velocity only. On the scale of the seperatrix the local behaviour of the probability density is linear.

22 Highlights of 2011 Journal of Physics A: Mathematical and Theoretical

accurate acoustic boundary conditions are obtained from a node-based Exploring Born–Infeld electrodynamics using lattice closure with local mass conservation and applicability for varying fluid viscosities. Data from an example simulation of a single oil drop in plasmas water interacting with a generated standing acoustic wave are presented and, where appropriate, compared with empirical theories and analogous D A Burton1,2, R M G M Trines1,3, T J Walton1,2 and H Wen1,2 calculations for a solid object. 1 Department of Physics, Lancaster University, Lancaster, UK Density maps from LB simulation of a 2 Cockcroft Institute, Daresbury, UK standing acoustic wave in water over

3 a period (T = 2π/ωs ≈ 265.8 time Rutherford Appleton Laboratory, Chilton, Didcot, UK steps) with an oil drop, starting at time step 7150. 2011 J. Phys. A: Math. Theor. 44 095501

The behaviour of large amplitude electrostatic waves in cold plasma is investigated in the context of Born–Infeld electrodynamics. Equations of motion for a relativistic electron fluid in a fixed ion background are established using an unconstrained action principle. A simple expression Differential geometric structures of stream for the maximum electric field of ‘quasi-static’ electric waves in a cold Born– Infeld plasma is deduced and its properties are analysed. A lower bound on functions: incompressible two-dimensional their wavelength is established and an approximation to their frequency is determined for ultrarelativistic phase velocities. flow and curvatures

K Yamasaki1, T Yajima2 and T Iwayama1 1 Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Nada ku, Kobe 657-8501, Japan 2 Department of Physics, Faculty of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo, 162-8601, Japan

2011 J. Phys. A: Math. Theor. 44 155501

The Okubo–Weiss field, frequently used for partitioning incompressible two- dimensional (2D) fluids into coherent and incoherent regions, corresponds to the Gaussian curvature of the stream function. Therefore, we consider the differential geometric structures of stream functions and calculate the The dashed curve shows μ versus ζ and the solid curve shows E versus ζ (not to scale). Points of Gaussian curvatures of some basic flows. We find the following. (I) The intersection of E with the ζ-axis are labelled I and III, and II is a turning point of E. Using (46) and q < 0 it follows dμ/dζ and E are of the opposite sign. vorticity corresponds to the mean curvature of the stream function. Thus, the stream-function surface for an irrotational flow and that for a parallel shear flow correspond to the minimal surface and a developable surface, respectively. (II) The relationship between the coherency and the magnitude Application of the multicomponent lattice of the vorticity is interpreted by the curvatures. (III) Using the Gaussian curvature, stability of single and double point vortex streets is analyzed. The Boltzmann simulation method to oil/water results of this analysis are compared with the well-known linear stability dispersions analysis. (IV) Conformal mapping in fluid mechanics is the physical expression of the geometric fact that the sign of the Gaussian curvature does not change in conformal mapping. These findings suggest that the 1,3 2 1 M A Seaton , I Halliday and A J Masters curvatures of stream functions are useful for understanding the geometric 1 School of Chemical Engineering and Analytical Science, The University of structure of an incompressible 2D flow. Manchester, Oxford Road, Manchester M13 9PL, UK 2 Materials and Engineering Research Institute, Sheffield Hallam University, Howard Street, Sheffield S1 1WB, UK 3 Present address: Computational Science and Engineering Department, STFC Daresbury Laboratory, Keckwick Lane, Daresbury, Warrington, Cheshire WA4 4AD, UK 575,174 2011 J. Phys. A: Math. Theor. 44 105502 Journal of Physics A: Mathematical

We study the propagation of acoustic fields in bounded, two-dimensional, and Theoretical full-text article mono-disperse oil/water emulsions using a carefully modified and downloads in 2011 appropriately calibrated single relaxation time multicomponent lattice Boltzmann equation simulation. Our model is a variant of an algorithm applying both interface forces based on macroscopic surface tensions and a kinematic condition for phase separation, adapted to allow sonic speed variations between its oil and water components. Appropriate second-order

Highlights of 2011 23 Journal of Physics A: Mathematical and Theoretical

Best Paper Prize

Since 2009, Journal of Physics A has awarded a Best Paper Prize, which serves to celebrate well written original research papers that make significant contributions to their fields.

The Editorial Board awarded the 2011 Best Paper Prize to the following papers, which were considered to excel in the criteria of novelty, achievement, potential impact and presentation.

Critical exponents of domain walls in the two-dimensional Potts model Jérôme Dubail, Jesper Lykke Jacobsen and Hubert Saleur 2010 J. Phys. A: Math. Theor. 43 482002

An infinite family of solvable and integrable quantum systems on a plane Frédérick Tremblay, Alexander V Turbiner and Pavel Winternitz 2009 J. Phys. A: Math. Theor. 42 242001

Thermodynamic Bethe ansatz for planar AdS/CFT: a proposal Diego Bombardelli, Davide Fioravanti and Roberto Tateo 2009 J. Phys. A: Math. Theor. 42 375401

You can read these papers and previous Best Paper Prize winners via the journal homepage.

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24 Highlights of 2011 Journal of Physics A: Mathematical and Theoretical

2011 special issues

Quantum integrable models and gauge-string duality Guest Editors: P Dorey, J Minahan and A Tseytlin 2011 J. Phys. A: Math. Theor. 44 issue 12 Remarkable progress has been achieved in the last 10 years in the quantitative understanding of gauge/string duality. The most studied example is the most symmetric example of a gauge-string duality—the correspondence between the maximally 5 supersymmetric gauge theory in flat 4 dimensions and superstring theory in a curved space AdS5×S , also referred to as AdS/ CFT duality. The solvability of this model, allowing us for example to compute the dimensions of gauge invariant operators for any value of the coupling, is due to its hidden integrability. The present special issue contains three long reviews that cover recent developments and also present a few particular directions in a detailed pedagogical manner.

Featuring the following papers

Integrability and the AdS/CFT correspondence Quantum integrability and functional equations: applications to the Didina Serban spectral problem of AdS/CFT and two-dimensional sigma models Dmytro Volin The method of finite-gap integration in classical and semi-classical string theory Benoît Vicedo

Scattering amplitudes in gauge theories: progress and outlook Guest Editors: Radu Roiban, Marcus Spradlin and Anastasia Volovich 2011 J. Phys. A: Math. Theor. 44 issue 45 This issue aims to serve as an introduction to our current understanding of the structure of scattering amplitudes in gauge theory, an area which has seen particularly rapid advances in recent years following decades of steady progress. The articles contained herein provide a snapshot of the latest developments which we hope will serve as a valuable resource for graduate students and other scientists wishing to learn about the current state of the field.

This issue features the following papers

Scattering amplitudes: the most perfect microscopic structures in the One-loop N = 4 super-Yang–Mills scattering amplitudes in d universe dimensions, relation to open strings and polygonal Wilson loops Lance J Dixon R M Schabinger

Tree-level formalism Scattering amplitudes and Wilson loops in twistor space Andreas Brandhuber, Bill Spence and Gabriele Travaglini Tim Adamo, Mathew Bullimore, Lionel Mason and David Skinner

Basics of generalized unitarity SUSY Ward identities, superamplitudes and counterterms Zvi Bern and Yu-tin Huang Henriette Elvang, Daniel Z Freedman and Michael Kiermaier

Generic multiloop methods and application to N = 4 super-Yang– Tree-level amplitudes and dual superconformal symmetry Mills J M Drummond John Joseph M Carrasco and Henrik Johansson Dual conformal symmetry at loop level: massive regularization Susy theories and QCD: numerical approaches Johannes M Henn Harald Ita Exact superconformal and Yangian symmetry of scattering amplitudes Loop amplitudes in gauge theories: modern analytic approaches Till Bargheer, Niklas Beisert and Florian Loebbert Ruth Britto Integrable spin chains and scattering amplitudes J Bartels, L N Lipatov and A Prygarin

Highlights of 2011 25 Journal of Physics A: Mathematical and Theoretical Journal of Physics A: Mathematical and Theoretical

Forthcoming special issues for 2012

Coherent states: mathematical and physical aspects

Guest Editors: S Twareque Ali, Jean-Pierre Antoine, Fabio Bagarello and Jean-Pierre Gazeau

Applications of zeta functions and other spectral functions in mathematics and physics: a special issue in honour of Stuart Dowker’s 75th birthday

Guest Editors: Fay Dowker, Emilio Elizalde and Klaus Kirsten

Quantum physics with non-Hermitian operators

Guest Editors: Carl Bender, Andreas Fring, Uwe Guenther and Hugh Jones

Lattice models and integrability: a special issue in honour of F Y Wu

Guest Editors: Anthony Guttmann and Jesper Lykke Jacobsen

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