DOCSLIB.ORG

Particle Creation and Memory Effects in a Trapped Ion Quantum Simulator

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Particle Creation and Memory Effects in a Trapped Ion Quantum Simulator Albert-Ludwigs-Universität Freiburg Particle creation and memory effects in a trapped ion quantum simulator Matthias Wittemer Dissertation zur Erlangung des Doktorgrades der Fakultät für Mathematik und Physik der Albert-Ludwigs-Universität Freiburg 2019 Dekan: Prof. Dr. Wolfgang Soergel Betreuer und Erstgutachter: Prof. Dr. Tobias Schätz Zweitgutachter: apl. Prof. Dr. Bernd von Issendorff Tag der mündlichen Prüfung: 16. Dezember 2019 Prüfer: Prof. Dr. Marc Schumann apl. Prof. Dr. Thomas Filk Prof. Dr. Tobias Schätz Zusammenfassung Die fundamentalen Gesetze der Quantenmechanik sind von unseren Alltagserfahrun- gen weit entfernt. Sie sind jedoch hervorragend geeignet um Beobachtungen in mikro- skopisch kleinen physikalischen Systemen zu erklären und vorherzusagen und werden daher bereits für verschiedene Anwendungen genutzt. Darüber hinaus wird, in Kom- bination mit relativistischen Überlegungen, grundlegenden Phänomenen der Quan- tenmechanik eine zentrale Rolle in der Entwicklung unseres Universums zugespro- chen. In der vorliegenden Arbeit verwenden wir einen Quantensimulator basierend auf gefangenen Ionen, um zwei fundamentale quantenmechanische Effekte, die seit vielen Jahrzehnten umfangreich studiert werden, zu untersuchen. In unserer ersten Untersuchung implementieren wir nicht-adiabatische Änderungen des Fallenpotenti- als der Ionen, um Fluktuationen des Quantenvakuums zu verstärken. Theoretischen Arbeiten zufolge lässt sich dieser Mechanismus als Analogie zur Teilchenerzeugung während der inflationären Phase des jungen Universums interpretieren. Solche Teil- chen gelten als Keime für die Bildung der makroskopischen Strukturen unseres heu- tigen Universums. In unserer analogen Quantensimulation wird die Erzeugung dieser Teilchen durch die Anregung eines gequetschten Zustands in der Bewegung der Io- nen nachgewiesen. Ein bemerkenswertes Merkmal dieses Mechanismus ist die damit einhergehende Erzeugung einer Quantenverschränkung. Im Falle der kosmologischen Teilchen erstreckt sich diese Verschränkung über große, kosmische Entfernungen. In unserer zweiten Untersuchung betrachten wir das Konzept offener Quantensysteme mit einem möglichst einfachen System und unter nahezu idealen Bedingungen. Jedes natürliche Quantensystem interagiert unweigerlich mit seiner Umgebung und kann da- her nicht als isoliertes, sondern nur als offenes Quantensystem, welches Korrelationen mit seiner Umgebung aufbauen kann, betrachtet werden. Wir definieren ein offenes Zwei-Niveau-System im elektronischen Freiheitsgrad eines einzelnen gefangenen Ions, welches wir an eine bosonische Umgebung, bestehend aus einem Bewegungsfreiheits- grad des Ions, koppeln. Zudem implementieren wir eine einstellbare Wechselwirkung zwischen System und Umgebung, welche zur Verschränkung dieser beiden Systeme führt. Indem wir Messungen nur am offenen Quantensystem vollziehen beobachten wir nicht-Markov’sches Verhalten, welches wir mit einem rigoros definierten Maß quanti- fizieren. Dabei decken wir auf, dass die Quantifizierung solcher Quantengedächtnis- effekte durch intrinsische quantenmechanische Messunsicherheiten limitiert ist. Die Untersuchungen, die wir in der vorliegenden Arbeit präsentieren, erweitern die Mög- lichkeiten unserer Ionenfallen-Apparatur analoge Quantensimulationen fundamenta- ler Probleme der Quantenmechanik unter nahezu idealen Bedingungen durchzuführen immens. Darüber hinaus werden zukünftige Studien komplexerer Sachverhalte in rea- listischen Quantensystemen ermöglicht. Abstract The fundamental laws of quantum mechanics are far from our everyday life experi- ences. However, they have been extremely successful in explaining observations in mi- croscopic physical systems and are, already, harnessed for several applications. More- over, in combination with relativistic considerations, basic phenomena from quantum mechanics are accredited a central role in the (macroscopic) evolution of our universe. In this thesis, we employ a trapped ion quantum simulator to experimentally investi- gate two fundamental quantum mechanical effects that have been extensively studied for many decades. In the first investigation, we implement non-adiabatic changes of the ions’ trapping potential in order to amplify quantum vacuum fluctuations. Fol- lowing theoretical works by others, this mechanism can be interpreted as an analog to the creation of particles during cosmic inflation in the early universe. Such cosmologi- cal particles are considered as the seeds for the formation of the large-scale structures in our universe that we observe nowadays. In our analog quantum simulation, the creation of particles is evidenced by the detection of a squeezed state in the motion of the ions. A remarkable feature of this mechanism is the accompanying creation of quantum entanglement. In case of the cosmological particles, this entanglement spreads over large, cosmic distances. In the second investigation, we benchmark a theoretical concept in the framework of open quantum systems in a most basic system and under near-ideal conditions. In nature, any quantum system inevitably interacts with its environment and, thereby, needs ultimately to be considered an open system that can build up correlations and, even, entanglement with its environment. We im- plement a spin-1/2 system in the electronic degree of freedom of a single trapped ion, which we couple to a bosonic environment, formed by a motional degree of freedom of the ion. Further, we implement a tunable interaction between system and envi- ronment that, in turn, can lead to entanglement. By performing measurements on the open system only, we observe quantum non-Markovian behavior, which we quan- tify using a rigorously defined measure. Thereby, we reveal that the quantification of such quantum memory effects is fundamentally limited by fundamental quantum mechanical measurement uncertainties. The investigations presented in this thesis significantly expand the capabilities of our trapped ion platform to perform analog quantum simulations of fundamental quantum mechanical problems under near-ideal conditions, and enable future studies of increased complexity and under more realistic conditions. Contents 1 Introduction1 2 Theoretical concepts7 2.1 Quantum mechanics basics . .7 2.2 Cosmology . 16 2.3 Open quantum systems . 21 3 Experimental methods 25 3.1 Experimental setup . 25 3.2 Spin control . 42 3.3 Phonon control . 49 3.4 Spin-phonon coupling . 62 3.5 Numerical calculations . 69 4 Experiments and results 77 4.1 Phonon pair creation . 77 4.2 Quantum memory effects . 104 5 Conclusion and outlook 117 Bibliography 121 1 Introduction To this day, quantum mechanics is our best way to describe nature at the smallest length scales. Since its development in the early 20th century, see, e.g., the works by Dirac (1930) and von Neumann (1932), the theory has made remarkable achievements in explaining and predicting phenomena that are far from our everyday experiences. Today, intriguing effects like quantum entanglement are routinely observed and har- nessed for multiple applications in well isolated and microscopic physical systems. However, physicists as well as philosophers have been wondering how the fundamen- tal laws can be translated into the macroscopic (classical) description of our world, see Bohr (1920) and Schrödinger (1926), which lead Schrödinger to his famous thought experiment (Schrödinger, 1935), addressing the bizarre consequences of such transla- tions onto macroscopic and even living objects. The fundamental laws of quantum mechanics have even more intriguing conse- quences when considered under relativistic conditions. Employing the framework of quantum field theory, such approaches give rise to phenomena like the Sauter- Schwinger effect (Sauter, 1931, 1932; Schwinger, 1951), Hawking radiation (Hawking, 1974, 1975), and the Unruh effect (Fulling, 1973; Davies, 1975; Unruh, 1976). All of these effects, and also other related phenomena like the static Casimir effect (Casimir, 1948) as well as its dynamical counter-part (Moore, 1970), have their origin in the intriguing description of the vacuum according to quantum field theory. While the vacuum is classically often considered as a space that is entirely devoid of matter, according to quantum field theory, the vacuum is not empty but filled with ubiqui- tous fluctuations. Taking account for Heisenberg’s uncertainty principle (Heisenberg, 1927), these fluctuations can be pictured as the random creation and annihilation of pairs of virtual particles. Certain, often considered extreme, conditions acting on the quantum fields corresponding to these particles, may then lead to the effects above. In recent theoretical investigations quantum fluctuations have been accredited an in- creasingly central role in the formation and evolution of our universe, see Brout et al. (1978), García-Bellido (1999), and Martin (2019). One key aspect of such considera- tions is the cosmological creation of pairs of particles in curved space-time, see Parker (1968) and Birrell and Davies (1982), and also Schrödinger (1939). In particular, during a period of cosmic expansion in the early universe, quantum fluctuations have been torn apart and amplified, and are considered to be responsible for the cosmic large-scale structures observable nowadays, cf. Liddle and Lyth (2000). Moreover, it is even considered that the creation of particles under these extreme conditions is 2 1 Introduction accompanied by the formation of quantum entanglement at large, cosmic distances (Martín-Martínez and Menicucci, 2012). Thus, Einstein’s phrasing
Load more

Recommended publications
  • Arxiv:0809.1487V2 [Cond-Mat.Stat-Mech] 25 Oct 2008 the first Two Authors Acknowledge Equal Contributions to This Review
    Advances in Physics Vol. 00, No. 00, Month-Month 200x, 1–111 Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques P. B. Blakiea∗, A. S. Bradleya;b, M. J. Davisb, R. J. Ballagha, and C. W. Gardinera aJack Dodd Centre for Quantum Technology, Department of Physics, University of Otago, Dunedin, New Zealand; bThe University of Queensland, School of Physical Sciences, ARC Centre of Excellence for Quantum-Atom Optics, Qld 4072, Australia (Received 00 Month 200x; In final form 00 Month 200x) We review phase space techniques based on the Wigner representation that provide an approximate description of dilute ultra-cold Bose gases. In this approach the quantum field evolution can be represented using equations of motion of a similar form to the Gross-Pitaevskii equation but with stochastic modifications that include quantum effects in a controlled degree of approximation. These techniques provide a practical quantitative description of both equilibrium and dynamical properties of Bose gas systems. We develop versions of the formalism appropriate at zero temperature, where quantum fluctuations can be important, and at finite temperature where thermal fluctuations dominate. The numerical techniques necessary for implementing the formalism are discussed in detail, together with methods for extracting observables of interest. Numerous applications to a wide range of phenomena are presented. Keywords: Ultra-cold Bose gas, quantum and finite temperature dynamics. ∗Corresponding author. Email: [email protected] arXiv:0809.1487v2 [cond-mat.stat-mech] 25 Oct 2008 The first two authors acknowledge equal contributions to this review. 2 Contents 1. Introduction 4 2. Background formalism 7 2.1.
    [Show full text]
  • Quantum Markov Chain Mixing and Dissipative Engineering
    Quantum Markov Chain Mixing and Dissipative Engineering Kastoryano, Michael James Publication date: 2012 Document version Early version, also known as pre-print Citation for published version (APA): Kastoryano, M. J. (2012). Quantum Markov Chain Mixing and Dissipative Engineering. Download date: 27. Sep. 2021 FACULTY OF SCIENCE UNIVERSITY OF COPENHAGEN Quantum Markov Chain Mixing and Dissipative Engineering PhD thesis Michael James Kastoryano The PhD School of Science Quantum Information Group QUANTOP – Danish National Research Foundation Centre for Quantum Optics Niels Bohr Institute and Niels Bohr International Academy Academic supervisors: Michael M. Wolf and Anders S. Sørensen December, 2011 Quantum Markov Chain Mixing and Dissipative Engineering Michael James Kastoryano This thesis is submitted in partial fulfilment of the requirements for the Ph.D. degree at the University of Copenhagen. Copyright c 2011 Michael James Kastoryano Abstract This thesis is the fruit of investigations on the extension of ideas of Markov chain mixing to the quantum setting, and its application to problems of dissipative engineering. A Markov chain describes a statistical process where the probability of future events depends only on the state of the system at the present point in time, but not on the history of events. Very many important processes in nature are of this type, therefore a good understanding of their behavior has turned out to be very fruitful for science. Markov chains always have a non-empty set of limiting distributions (stationary states). The aim of Markov chain mixing is to obtain (upper and/or lower) bounds on the number of steps it takes for the Markov chain to reach a stationary state.
    [Show full text]
  • Exact Calculation of Entanglement in a 19-Site 2D Spin System
    Exact Calculation of Entanglement in a 19-site 2D Spin System Qing Xu,1 Sabre Kais∗,2 Maxim Naumov,3 and Ahmed Sameh3 1Department of Physics, Purdue University, West Lafayette, Indiana 47907, USA 2Department of Chemistry and Birck Nanotechnology center, Purdue University, West Lafayette, Indiana 47907, USA 3Department of Computer Science, Purdue University, West Lafayette, Indiana 47907, USA (Dated: October 22, 2018) Using the Trace Minimization Algorithm, we carried out an exact calculation of entanglement in 1 a 19-site two-dimensional transverse Ising model. This model consists of a set of localized spin- 2 particles in a two dimensional triangular lattice coupled through exchange interaction J and subject to an external magnetic field of strength h. We demonstrate, for such a class of two-dimensional magnetic systems, that entanglement can be controlled and tuned by varying the parameter λ = h/J in the Hamiltonian and by introducing impurities into the systems. Examining the derivative of the concurrence as a function of λ shows that the system exhibits a quantum phase transition at about λc = 3.01, a transition induced by quantum fluctuations at the absolute zero of temperature. PACS numbers: 03.67.Mn I. INTRODUCTION Entanglement, which is a quantum mechanical property that has no classical analog, has been viewed as a resource of quantum information and computation [1–8]. Intensive researches of entanglement measurement, entanglement monotone, criteria for distinguishing separable from entangled pure states and all the extensions from bipartite to multipartite systems have been carried out both qualitatively and quantitatively [1]. At the interface between quantum information and statistical mechanics, there has been particular analysis of entanglement in quantum critical models [9–12].
    [Show full text]
  • Relativistic Fluid Dynamics
    Living Reviews in Relativity (2021) 24:3 https://doi.org/10.1007/s41114-021-00031-6 REVIEW ARTICLE Relativistic fluid dynamics: physics for many different scales Nils Andersson1 · Gregory L. Comer2 Received: 1 June 2020 / Accepted: 22 January 2021 © The Author(s) 2021 Abstract The relativistic fluid is a highly successful model used to describe the dynam- ics of many-particle systems moving at high velocities and/or in strong gravity. It takes as input physics from microscopic scales and yields as output predictions of bulk, macroscopic motion. By inverting the process—e.g., drawing on astrophysi- cal observations—an understanding of relativistic features can lead to insight into physics on the microscopic scale. Relativistic fluids have been used to model sys- tems as “small” as colliding heavy ions in laboratory experiments, and as large as the Universe itself, with “intermediate” sized objects like neutron stars being considered along the way. The purpose of this review is to discuss the mathematical and theo- retical physics underpinnings of the relativistic (multi-) fluid model. We focus on the variational principle approach championed by Brandon Carter and collaborators, in which a crucial element is to distinguish the momenta that are conjugate to the particle number density currents. This approach differs from the “standard” text-book deriva- tion of the equations of motion from the divergence of the stress-energy tensor in that one explicitly obtains the relativistic Euler equation as an “integrability” condition on the relativistic vorticity. We discuss the conservation laws and the equations of motion in detail, and provide a number of (in our opinion) interesting and relevant applications This article is a revised version of https://doi.org/10.12942/lrr-2007-1.
    [Show full text]
  • Cluster Mechanisms in the Fully Frustrated Ising Model
    Cluster mechanisms in the fully frustrated Ising model Werner Kerler and Peter Rehberg Fachbereich Physik, Universit¨at Marburg, D-35032 Marburg, Germany Abstract The cluster algorithm in the fully frustrated Ising model on the square lattice is essentially different from the ones used in other systems. Thus its better understanding is particularly important for finding new lines of development. Therefore we investigate it in detail. In our simulations of high statistics more appropriate choices of the probability for freezing bonds and of that for flipping spins are seen to lead to better results. In an analysis of the arXiv:cond-mat/9401063v1 27 Jan 1994 topological properties we derive a set of rules for possible cluster configurations and give a classification by pairs of winding numbers. 1 I. Introduction Cluster algorithms, introduced by Swendsen and Wang [1] for ferromagnetic Potts models, allow a considerable reduction of critical slowing down in Monte Carlo simulations. Beginning with O(n)-models [2] and φ4-theory [3] various embeddings of the Ising dynamics have also been successful. In the ferromagnetic Ising model in two dimensions forming blocks of spins [4] has been shown to lead to an improvement. The treatments of Z2 gauge theories in three dimensions [5], which use plaquette variables, profit from the duality to the respective spin models. The combination of cluster dynamics with making the strength parameter dynamical recently has led to a very efficient method [6] to treat first order phase transitions in the Potts model. The algorithm for the fully frustrated Ising model on the square lattice in two dimensions found by Kandel, Ben-Av, and Domany [7, 8] is of rather different type.
    [Show full text]
  • Quantum Simulations of Out-Of-Equilibrium Phenomena
    Technische Universitat¨ Munchen¨ Max-Planck–Institut f¨ur Quantenoptik Quantum Simulations of Out-of-Equilibrium Phenomena Birger Christian Helge Horstmann Vollst¨andiger Abdruck der von der Fakult¨at f¨ur Physik der Technischen Universit¨at M¨unchen zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigten Dissertation. Vorsitzende : Univ.-Prof. Dr. K. Krischer Pr¨ufer der Dissertation : 1. Hon.-Prof. I. Cirac, Ph.D. 2. Univ.-Prof. J. von Delft, Ph.D. 3. Ludwig-Maximilians-Universit¨at M¨unchen Die Dissertation wurde am 07.03.2011 bei der Technischen Universit¨at M¨unchen eingereicht und durch die Fakult¨at f¨ur Physik am 30.03.2011 angenommen. Abstract The quantum world contains many counterintuitive phenomena and trig- gers the development of new technologies. Unfortunately, in most cases classical numerical simulations of quantum systems are intractable. A quantum simulator addresses this problem by running the simulation on a quantum system. In this thesis we discuss three proposals for quantum simulators of the following out-of-equilibrium phenomena: Anderson lo- calization in disordered systems, dissipative quantum phase transitions, and Hawking radiation emitted by black holes. We propose to realize Anderson localization of ultracold atoms in an optical lattice with a disorder potential generated via a secondary species frozen in a superposition of random configurations. We investigate two preparation schemes: the independent preparation of both species and the transfer of a part of the population into a different internal state, for bosonic gases with infinite and weak intra-species interactions. In all setups we observe dynamical localization, i.e., the wavefunctions of the steady states feature exponential tails and reduced coherence.
    [Show full text]
  • A Maximum Entropy Model of Phonotactics and Phonotactic Learning
    A Maximum Entropy Model of Phonotactics and Phonotactic Learning Bruce Hayes Colin Wilson [email protected] [email protected] Preprint version, August 2007 Abstract The study of phonotactics (e.g., the ability of English speakers to distinguish possible words like blick from impossible words like *bnick) is a central topic in phonology. We propose a theory of phonotactic grammars and a learning algorithm that constructs such grammars from positive evidence. Our grammars consist of constraints that are assigned numerical weights according to the principle of maximum entropy. Possible words are assessed by these grammars based on the weighted sum of their constraint violations. The learning algorithm yields grammars that can capture both categorical and gradient phonotactic patterns. The algorithm is not provided with any constraints in advance, but uses its own resources to form constraints and weight them. A baseline model, in which Universal Grammar is reduced to a feature set and an SPE-style constraint format, suffices to learn many phonotactic phenomena. In order to learn nonlocal phenomena such as stress and vowel harmony, it is necessary to augment the model with autosegmental tiers and metrical grids. Our results thus offer novel, learning-theoretic support for such representations. We apply the model to English syllable onsets, Shona vowel harmony, quantity-insensitive stress typology, and the full phonotactics of Wargamay, showing that the learned grammars capture the distributional generalizations of these languages and accurately predict the findings of a phonotactic experiment. Keywords: phonotactics, maximum entropy, learnability, onsets, Shona, Wargamay Hayes/Wilson Maximum Entropy Phonotactics p. 2 1. Introduction* In one of the central articles from the early history of generative phonology, Chomsky and Halle (1965) lay out a research program for the theory of phonotactics.
    [Show full text]
  • Biomolecular Force Fields: Where Have We Been, Where Are We Now, Where Do We Need to Go and How Do We Get There?
    Journal of Computer-Aided Molecular Design https://doi.org/10.1007/s10822-018-0111-4 PERSPECTIVE Biomolecular force fields: where have we been, where are we now, where do we need to go and how do we get there? Pnina Dauber‑Osguthorpe2 · A. T. Hagler1,3 Received: 17 November 2017 / Accepted: 9 March 2018 © Springer Nature Switzerland AG 2018 Abstract In this perspective, we review the theory and methodology of the derivation of force fields (FFs), and their validity, for molecular simulations, from their inception in the second half of the twentieth century to the improved representations at the end of the century. We examine the representations of the physics embodied in various force fields, their accuracy and defi- ciencies. The early days in the 1950s and 60s saw FFs first introduced to analyze vibrational spectra. The advent of computers was soon followed by the first molecular mechanics machine calculations. From the very first papers it was recognized that the accuracy with which the FFs represented the physics was critical if meaningful calculated structural and thermodynamic properties were to be achieved. We discuss the rigorous methodology formulated by Lifson, and later Allinger to derive molecular FFs, not only obtain optimal parameters but also uncover deficiencies in the representation of the physics and improve the functional form to account for this physics. In this context, the known coupling between valence coordinates and the importance of coupling terms to describe the physics of this coupling is evaluated. Early simplified, truncated FFs introduced to allow simulations of macromolecular systems are reviewed and their subsequent improvement assessed.
    [Show full text]
  • On Generalized Cluster Algorithms for Frustrated Spin Models
    SCCS-527 On generalized cluster algorithms for frustrated spin models P.D. Coddington Northeast Parallel Architectures Center, 111 College Place, Syracuse University, Syracuse, NY 13244, U.S.A. L. Han Physics Department, Syracuse University, Syracuse, NY 13244, U.S.A. November 5, 1993 Standard Monte Carlo cluster algorithms have proven to be very effective for many different spin models, however they fail for frustrated spin systems. Recently a gen- eralized cluster algorithm was introduced that works extremely well for the fully frustrated Ising model on a square lattice, by placing bonds between sites based on information from plaquettes rather than links of the lattice. Here we study some prop- arXiv:cond-mat/9402030v1 7 Feb 1994 erties of this algorithm and some variants of it. We introduce a practical methodology for constructing a generalized cluster algorithm for a given spin model, and inves- tigate apply this method to some other frustrated Ising models. We find that such algorithms work well for simple fully frustrated Ising models in two dimensions, but appear to work poorly or not at all for more complex models such as spin glasses. 1 I. INTRODUCTION The cluster update algorithms of Swendsen and Wang [1] and Wolff [2] can provide a great improvement in computational efficiency over the Metropolis algorithm [3,4] and other local Monte Carlo update schemes. Due to the non-local nature of the cluster algorithms, which update large clusters of spins at a time, they are very effective at decorrelating suc- cessive configurations and can therefore greatly reduce critical slowing down [4,5] in certain ferromagnetic and anti-ferromagnetic spin models.
    [Show full text]
  • Arxiv:2102.04557V3 [Cond-Mat.Dis-Nn] 27 Mar 2021 Updates , and Modern Extensions of This Methodology During Dynamics, Without Any Algorithmic Aid1
    Non-equilibrium criticality and efficient exploration of glassy landscapes with memory dynamics Yan Ru Pei1, ∗ and Massimiliano Di Ventra1, y 1Department of Physics, University of California, San Diego La Jolla, CA 92093 Spin glasses are notoriously difficult to study both analytically and numerically due to the presence of frustration and metastability. Their highly non-convex landscapes require collective updates to explore efficiently. Currently, most state-of-the-art algorithms rely on stochastic spin clusters to perform non-local updates, but such \cluster algorithms" lack general efficiency. Here, we introduce a non-equilibrium approach for simulating spin glasses based on classical dynamics with memory. By simulating various classes of 3d spin glasses (Edwards-Anderson, partially-frustrated, and fully- frustrated models), we find that memory dynamically promotes critical spin clusters during time evolution, in a self-organizing manner. This facilitates an efficient exploration of the low-temperature phases of spin glasses. I. INTRODUCTION which proved to be very effective for the 2d ferro- magnetic Ising model. Unfortunately, despite several The study of spin glasses has contributed substantially modifications made to account for the non-locality of 25,26 to our understanding of a wide variety of phenomena1{3, frustration , these cluster algorithms still struggle for much beyond the complex magnetic models for which high-dimensional glasses. The main reason behind their they were first introduced4. In their most basic form, inefficiency is the tendency for the cluster percolation these systems are described by the following simple process to be persistently hyper-critical, due to a mis- Hamiltonian5: match of critical temperature and cluster percolation ratio27,28.
    [Show full text]
  • Invaded Cluster Dynamics for Frustrated Models
    Invaded Cluster Dynamics for Frustrated Models Giancarlo Franzese, Vittorio Cataudella and Antonio Coniglio∗ Dipartimento di Scienze Fisiche, Universit`a“Federico II”, Mostra d’Oltremare Pad.19 I-80125 Napoli, Italy, INFM - unit`adi Napoli and ∗ INFN - sezione di Napoli (June 16, 2021) Abstract The Invaded Cluster (IC) dynamics introduced by Machta et al. [Phys. Rev. Lett. 75 2792 (1995)] is extended to the fully frustrated Ising model on a square lattice. The properties of the dynamics which exhibits numerical evidence of self-organized criticality are studied. The fluctuations in the IC dynamics are shown to be intrinsic of the algorithm and the fluctuation- dissipation theorem is no more valid. The relaxation time is found very short and does not present critical size dependence. Ref-no. DSF-T-30/97 arXiv:cond-mat/9707008v2 [cond-mat.stat-mech] 10 Sep 1997 1 I. INTRODUCTION Recently a new type of cluster Monte Carlo (MC) dynamics, the Invaded Cluster (IC) dynamics, based on invaded percolation has been introduced by Machta et al. for the ferro- magnetic Ising model. [1] The IC dynamics is based on the Kastelein-Fortuin and Coniglio- Klein (KF-CK) cluster formulation of the Ising model [2] and has been shown to be even more efficient than the Swendsen-Wang (SW) dynamics [3] in equilibrating the system at the critical temperature. The IC dynamics has the advantage that the value of the critical temperature does not need to be known a priori. In fact the dynamics itself drives the system to the critical region as in self-organized critical (SOC) systems.
    [Show full text]
  • Relativistic Lattice Boltzmann Methods: Theory and Applications
    Relativistic Lattice Boltzmann Methods: Theory and Applications. A. Gabbana 1 Universit`adi Ferrara and INFN-Ferrara, I-44122 Ferrara, Italy Bergische Universit¨atWuppertal, D-42119 Wuppertal, Germany D. Simeoni Universit`adi Ferrara and INFN-Ferrara, I-44122 Ferrara, Italy Bergische Universit¨atWuppertal, D-42119 Wuppertal, Germany University of Cyprus, CY-1678 Nicosia, Cyprus S. Succi Center for Life Nano Science @ La Sapienza, Italian Institute of Technology, Viale Regina Elena 295, I-00161 Roma, Italy Istituto Applicazioni del Calcolo, National Research Council of Italy, Via dei Taurini 19, I-00185 Roma, Italy R. Tripiccione Universit`adi Ferrara and INFN-Ferrara, I-44122 Ferrara, Italy Abstract We present a systematic account of recent developments of the relativistic Lattice Boltzmann method (RLBM) for dissipative hydrodynamics. We describe in full detail a unified, compact and dimension-independent procedure to design relativistic LB schemes capable of bridging the 2 2 gap between the ultra-relativistic regime, kBT mc , and the non-relativistic one, kBT mc . We further develop a systematic derivation of the transport coefficients as a function of the kinetic relaxation time in d = 1; 2; 3 spatial dimensions. The latter step allows to establish a quantitative bridge between the parameters of the kinetic model and the macroscopic transport coefficients. This leads to accurate calibrations of simulation parameters and is also relevant at the theoretical level, as it provides neat numerical evidence of the correctness of the Chapman-Enskog procedure. We present an extended set of validation tests, in which simulation results based on the RLBMs 2 arXiv:1909.04502v2 [hep-lat] 28 May 2020 are compared with existing analytic or semi-analytic results in the mildly-relativistic (kBT ∼ mc ) regime for the case of shock propagations in quark-gluon plasmas and laminar electronic flows in ultra-clean graphene samples.
    [Show full text]