DOCSLIB.ORG

Macroscopic Quantum Phenomena in Interacting Bosonic Systems: Josephson flow in Liquid 4He and Multimode Schr¨Odingercat States

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Macroscopic Quantum Phenomena in Interacting Bosonic Systems: Josephson flow in Liquid 4He and Multimode Schr¨Odingercat States Macroscopic quantum phenomena in interacting bosonic systems: Josephson flow in liquid 4He and multimode Schr¨odingercat states by Tyler James Volkoff A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Chemistry in the Graduate Division of the University of California, Berkeley Committee in charge: Professor K. Birgitta Whaley, Chair Professor Philip L. Geissler Professor Richard E. Packard Fall 2014 Macroscopic quantum phenomena in interacting bosonic systems: Josephson flow in liquid 4He and multimode Schr¨odingercat states Copyright 2014 by Tyler James Volkoff 1 Abstract Macroscopic quantum phenomena in interacting bosonic systems: Josephson flow in liquid 4He and multimode Schr¨odingercat states by Tyler James Volkoff Doctor of Philosophy in Chemistry University of California, Berkeley Professor K. Birgitta Whaley, Chair In this dissertation, I analyze certain problems in the following areas: 1) quantum dynam- ical phenomena in macroscopic systems of interacting, degenerate bosons (Parts II, III, and V), and 2) measures of macroscopicity for a large class of two-branch superposition states in separable Hilbert space (Part IV). Part I serves as an introduction to important concepts recurring in the later Parts. In Part II, a microscopic derivation of the effective action for the relative phase of driven, aperture-coupled reservoirs of weakly-interacting condensed bosons from a (3 + 1)D microscopic model with local U(1) gauge symmetry is presented. The effec- tive theory is applied to the transition from linear to sinusoidal current vs. phase behavior observed in recent experiments on liquid 4He driven through nanoaperture arrays. Part III discusses path-integral Monte Carlo (PIMC) numerical simulations of quantum hydrody- namic properties of reservoirs of He II communicating through simple nanoaperture arrays. In addition to calculating the local superfluid density in these systems, new estimators for hydrodynamic observables and novel methods for extracting the length scale characterizing the decay of superfluidity at the system boundary from PIMC data are introduced with the aim of exploring the mechanism of superfluid weak-link formation in nanoscale containers. Part IV consists of an analysis of macroscopicity measures for a large class of Schr¨odinger cat states of N-mode photonic systems. For cat states of this class, it is shown that a well- known measure of superposition size based on the optimal distinguishability of the branches and another based on metrological usefulness of the superposition relative to its branches agree (i.e., designate the same superpositions as macroscopic) when the inner product of the branches of the superposition is sufficiently small. For certain superpositions in this class, a technique is presented for deriving a state-specific metrological macroscopicity algebra of observables. The dynamics of superposition size measures is also considered, leading to the notion of \distinguishability time," a generalization of the orthogonalization times of Mandelstam-Tamm and Margolus-Levitin. In Part V, an investigation of the nonequilibrium dynamics of a quantum dot-Josephson junction-quantum dot nanodevice is presented. The nonequilibrium action of the system is 2 calculated by making use of the Keldysh formalism and a potential use of the device for transferring macroscopic superposition states between a spin-system and an s-wave super- conductor is discussed. i Contents Acknowledgements iv Notation and list of acronyms vi Preface vii I Introduction 1 1 Quantum states of many-boson systems 2 1.1 Fock space . 2 1.1.1 Bosonic and fermionic Hilbert spaces . 2 1.1.2 Vacuum state and particle number sectors . 6 1.2 Heisenberg-Weyl coherent states . 7 1.2.1 Heisenberg-Weyl and oscillator Lie algebras . 8 1.2.2 Reduced density matrices and field operators . 9 1.2.3 Important quasiprobability distributions . 14 2 Interacting Bose gases 19 2.1 Weakly-interacting Bose gases (WIBG) . 19 2.1.1 ODLRO and Bogoliubov's approximation . 20 2.1.2 Popov approximation . 24 2.2 Liquid 4He..................................... 25 2.2.1 Landau critical velocity and Hess-Fairbank effect . 27 2.2.2 From interacting bosons to two-fluid theory . 30 II Theory of Josephson oscillations in driven liquid 4He 33 3 Josephson effect from an action principle in driven He II 34 3.1 Gauge theory of the WIBG . 35 3.1.1 Construction of gauge invariant action . 42 3.1.2 Bosonic two-body Hubbard-Stratonovich transformation . 43 ii 3.2 Josephson effect in neutral bosonic liquids . 46 3.3 Effective action for gauged WIBG . 50 3.3.1 Self-consistent Hubbard-Stratonovich field . 54 3.3.2 Gauge invariant Josephson-Anderson equation . 55 3.3.3 Fluxoid quantization, Hess-Fairbank equation . 59 3.3.4 Tunneling contribution for multiaperture arrays . 64 3.3.5 Discussion of effective action . 65 3.4 Current phase relations . 66 3.4.1 Current phase relation for two-aperture array . 70 3.5 Low energy current phase relations . 71 3.5.1 Weak-coupling RG approach . 71 3.5.2 Background field RG approach . 73 3.5.3 Single vs. multiple apertures . 78 3.6 Concluding remarks . 79 III Numerical simulations of constrained liquid 4He 82 4 The path integral (quantum) Monte Carlo method 83 4.1 Imaginary time picture and major approximations . 83 4.2 PIMC for weakly-coupled 4He reservoirs . 86 4.2.1 PIMC in cylindrical geometry . 87 4.3 Local hydrodynamic estimators . 89 4.3.1 Superfluid density . 89 4.3.2 Momentum and momentum correlations . 95 4.3.3 Circulation and vorticity . 101 4.3.4 Local and global healing lengths . 110 4.3.5 Evidence for weak-link formation . 115 IV Measures of superposition size in separable Hilbert space 121 5 How big is Schr¨odinger'scat? 122 5.1 Background on large quantum superposition states . 122 5.2 Superposition size via quantum binary distinguishability . 124 5.2.1 Distinguishability of branch n-RDMs . 128 5.3 Branch distinguishability examples . 131 5.3.1 General equal-amplitude two branch superpositions . 131 5.3.2 Entangled coherent states . 133 5.3.3 Gaussian product state superpositions . 138 5.3.4 Hierarchical and concatenated cat states . 141 5.3.5 (2 + 1)-D quantum critical superpositions . 144 iii 5.4 Other measurement-based measures . 147 5.4.1 Marquardt's measure . 147 5.4.2 Relative quantum Fisher information . 149 5.5 Comparison based measures . 153 5.6 Measures based on the Wigner function . 159 5.7 Entanglement of jΨi ............................... 161 6 Dynamical binary distinguishability 165 6.1 Mandelstam-Tamm uncertainty relation . 165 6.2 Margolus-Levitin orthogonalization time . 169 6.3 Independent branch evolution . 170 7 Deeper look at metrological macroscopicity 172 7.1 Spin systems . 172 7.1.1 Cat state basis for (C2)⊗N . 172 7.2 Algebras for metrological macroscopicity . 174 7.2.1 Entangled coherent states . 175 7.2.2 Multimode superposition of Fock states . 177 7.2.3 Hierarchical cat states . 177 7.2.4 Algebras for N rF macroscopicity . 179 7.2.5 General construction of jΨi with N rF (jΨi) > N . 181 V Functional integrals for QD-SNS-QD system 182 8 The QD-SNS-QD system 183 8.1 Motivation . 183 8.2 Coherent state path integrals for QD-SNS-QD . 185 8.2.1 Keldysh action for QD-SNS-SD system . 185 8.2.2 Equilibrium action for QD-SNS-QD system . 192 9 Conclusion 198 9.1 Looking ahead . 198 A Brief overview of the quantum Fisher information 201 A.1 Quantum Fisher information . 201 Bibliography 204 iv Acknowledgements This dissertation is dedicated to my family, especially to my mother and father. Through their exemplary work ethic and perseverance and love, they have provided a standard to which I am always trying to amend. Berkeley is a great place to do science mostly because of the large number of talented researchers, teachers, and visitors working there. It has been my pleasure to learn from their expertises. Of them all, I must firstly extend heartfelt thanks to my advisor, K. Birgitta Whaley (\Birgit"), for providing an excellent work environment and many opportunities for teaching and travel, and for encouraging my good ideas while amending the misguided ones and rejecting the bad ones. Her scientific influence is clearly present in the calculations and physical interpretations put forth in this dissertation. During my first semester at Berkeley, Birgit introduced me to Prof. Richard Packard because of my interest in the experiments conducted in his laboratory. Richard proceeded to instruct a personalized biweekly crash course into the rich field of superfluid dynamics; topics included vortex tangles and critical dynamics. I am thankful to him for his generous advice. Members of Richard's research group, Aditya Joshi in particular, provided valuable perspective on the experimental study of superfluids. Because of our extensive collaboration and his senior academic position, Yongkyung Kwon, of Konkuk University in Seoul, has acted as an ipso facto coadvisor. He graciously hosted me in his research group for a total of six months or so over the summers of 2011 and 2012; during the latter, he arranged a homestay for me which was an exciting immersion into Korean domestic life. His expertise in physical applications of quantum Monte Carlo techniques has been an instructive resource for me. His students, Sungjin Park and Hyeon- deok Shin, gave advice on a number of technical issues relating to path integral Monte Carlo simulations. My officemates in Hearst Memorial Mining Building and O'Brien Hall have been great sources of support and technical knowledge throughout my time in Berkeley. Conversations with Chris Herdman and longtime officemate Joel Corbo have been particularly instructive both academically and personally. I also thank Prof. Frank Wilhelm for teaching me about phenomena related to the Josephson effect in various types of weak link junctions between superconductors during one of his visits to Berkeley.
Load more
Loading...
Loading...
Loading...
Loading...
Loading...

223 pages remaining, click to load more.

Recommended publications
  • The Mechanics of the Fermionic and Bosonic Fields: an Introduction to the Standard Model and Particle Physics
    The Mechanics of the Fermionic and Bosonic Fields: An Introduction to the Standard Model and Particle Physics Evan McCarthy Phys. 460: Seminar in Physics, Spring 2014 Aug. 27,! 2014 1.Introduction 2.The Standard Model of Particle Physics 2.1.The Standard Model Lagrangian 2.2.Gauge Invariance 3.Mechanics of the Fermionic Field 3.1.Fermi-Dirac Statistics 3.2.Fermion Spinor Field 4.Mechanics of the Bosonic Field 4.1.Spin-Statistics Theorem 4.2.Bose Einstein Statistics !5.Conclusion ! 1. Introduction While Quantum Field Theory (QFT) is a remarkably successful tool of quantum particle physics, it is not used as a strictly predictive model. Rather, it is used as a framework within which predictive models - such as the Standard Model of particle physics (SM) - may operate. The overarching success of QFT lends it the ability to mathematically unify three of the four forces of nature, namely, the strong and weak nuclear forces, and electromagnetism. Recently substantiated further by the prediction and discovery of the Higgs boson, the SM has proven to be an extraordinarily proficient predictive model for all the subatomic particles and forces. The question remains, what is to be done with gravity - the fourth force of nature? Within the framework of QFT theoreticians have predicted the existence of yet another boson called the graviton. For this reason QFT has a very attractive allure, despite its limitations. According to !1 QFT the gravitational force is attributed to the interaction between two gravitons, however when applying the equations of General Relativity (GR) the force between two gravitons becomes infinite! Results like this are nonsensical and must be resolved for the theory to stand.
    [Show full text]
  • Physics of Three-Dimensional Bosonic Topological Insulators: Surface-Deconfined Criticality and Quantized Magnetoelectric Effect
    PHYSICAL REVIEW X 3, 011016 (2013) Physics of Three-Dimensional Bosonic Topological Insulators: Surface-Deconfined Criticality and Quantized Magnetoelectric Effect Ashvin Vishwanath Department of Physics, University of California, Berkeley, California 94720, USA Materials Science Division, Lawrence Berkeley National Laboratories, Berkeley, California 94720, USA T. Senthil Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA (Received 4 October 2012; revised manuscript received 31 December 2012; published 28 February 2013) We discuss physical properties of ‘‘integer’’ topological phases of bosons in D ¼ 3 þ 1 dimensions, protected by internal symmetries like time reversal and/or charge conservation. These phases invoke interactions in a fundamental way but do not possess topological order; they are bosonic analogs of free- fermion topological insulators and superconductors. While a formal cohomology-based classification of such states was recently discovered, their physical properties remain mysterious. Here, we develop a field-theoretic description of several of these states and show that they possess unusual surface states, which, if gapped, must either break the underlying symmetry or develop topological order. In the latter case, symmetries are implemented in a way that is forbidden in a strictly two-dimensional theory. While these phases are the usual fate of the surface states, exotic gapless states can also be realized. For example, tuning parameters can naturally lead to a deconfined quantum critical point or, in other situations, to a fully symmetric vortex metal phase. We discuss cases where the topological phases are characterized by a quantized magnetoelectric response , which, somewhat surprisingly, is an odd multiple of 2.Two different surface theories are shown to capture these phenomena: The first is a nonlinear sigma model with a topological term.
    [Show full text]
  • Clifford Algebras, Multipartite Systems and Gauge Theory Gravity
    Mathematical Phyiscs Clifford Algebras, Multipartite Systems and Gauge Theory Gravity Marco A. S. Trindadea Eric Pintob Sergio Floquetc aColegiado de Física Departamento de Ciências Exatas e da Terra Universidade do Estado da Bahia, Salvador, BA, Brazil bInstituto de Física Universidade Federal da Bahia Salvador, BA, Brazil cColegiado de Engenharia Civil Universidade Federal do Vale do São Francisco Juazeiro, BA, Brazil. E-mail: matrindade@uneb.br, ericpinto3@gmail.com, sergio.floquet@univasf.edu.br Abstract: In this paper we present a multipartite formulation of gauge theory gravity based on the formalism of space-time algebra for gravitation developed by Lasenby and Do- ran (Lasenby, A. N., Doran, C. J. L, and Gull, S.F.: Gravity, gauge theories and geometric algebra. Phil. Trans. R. Soc. Lond. A, 582, 356:487 (1998)). We associate the gauge fields with description of fermionic and bosonic states using the generalized graded tensor product. Einstein’s equations are deduced from the graded projections and an algebraic Hopf-like structure naturally emerges from formalism. A connection with the theory of the quantum information is performed through the minimal left ideals and entangled qubits are derived. In addition applications to black holes physics and standard model are outlined. arXiv:1807.09587v2 [physics.gen-ph] 16 Nov 2018 1Corresponding author. Contents 1 Introduction1 2 General formulation and Einstein field equations3 3 Qubits 9 4 Black holes background 10 5 Standard model 11 6 Conclusions 15 7 Acknowledgements 16 1 Introduction This work is dedicated to the memory of professor Waldyr Alves Rodrigues Jr., whose contributions in the field of mathematical physics were of great prominence, especially in the study of clifford algebras and their applications to physics [1].
    [Show full text]
  • Keference International Centre for Theoretical
    KEFERENCE INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS IC/86/342 INTERNATIONAL THE REGULAR EFFECTIVE ACTION OF GAUGE FIELD THEORY AND QUANTUM GRAVITY ATOMIC ENERGY AGENCY Nazir S. Baaklini UNITED NATIONS EDUCATIONAL, SCIENTIFIC AND CULTURAL ORGANIZATION IC/86/342 International Atomic Energy Agency 0. INTRODUCTION and The effective action of quantum field theory, defined by the functional United Nations Educational Scientific and Cultural Organization integral , is an elegant and potentially, very powerful framework for compu- INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS ting quantum effects, in a manner that preserves underlying fundamental symmetries. However, this framework had been utilized mainly in computing effective potentials, and in certain discussions of the divergent counter-terms needed in gauge field THE REGULAR EFFECTIVE ACTION OF GAUGE FIELD THEORY theory and quantum gravity. Whereas it should ~ae very fruitful fo develop expre- AND QUANTUM GRAVITY ssions for the effective action which could have general applicability, computa- tions are still performed using conventional Feynman rules. What is needed is a perturbative formalism for the effective action vhicii applies to a general field Nazir S. Baaklini theory containing Bosonic as well as Fermionic fields, and vhich could be used to International Centre for Theoretical Physics, Trieste, Italy address fundamental issues of quantum field theory and quantum gravity. and Dahr el Chir Science Centre, Dhour el Choueir, Lebanon. On the other hand, our study of the effective action makes impact on two fundamental issues. One of these concerns the treatment of gauge field theory and other singular systems. The other concerns the ultraviolet divergences of quantum field theory and quantum gravity.
    [Show full text]
  • Field Theory of Anyons and the Fractional Quantum Hall Effect 30- 50
    NO9900079 Field Theory of Anyons and the Fractional Quantum Hall Effect Susanne F. Viefers Thesis submitted for the Degree of Doctor Scientiarum Department of Physics University of Oslo November 1997 30- 50 Abstract This thesis is devoted to a theoretical study of anyons, i.e. particles with fractional statistics moving in two space dimensions, and the quantum Hall effect. The latter constitutes the only known experimental realization of anyons in that the quasiparticle excitations in the fractional quantum Hall system are believed to obey fractional statistics. First, the properties of ideal quantum gases in two dimensions and in particular the equation of state of the free anyon gas are discussed. Then, a field theory formulation of anyons in a strong magnetic field is presented and later extended to a system with several species of anyons. The relation of this model to fractional exclusion statistics, i.e. intermediate statistics introduced by a generalization of the Pauli principle, and to the low-energy excitations at the edge of the quantum Hall system is discussed. Finally, the Chern-Simons-Landau-Ginzburg theory of the fractional quantum Hall effect is studied, mainly focusing on edge effects; both the ground state and the low- energy edge excitations are examined in the simple one-component model and in an extended model which includes spin effets. Contents I General background 5 1 Introduction 7 2 Identical particles and quantum statistics 10 3 Introduction to anyons 13 3.1 Many-particle description 14 3.2 Field theory description
    [Show full text]
  • The New Bosonic Mechanism Rostislav Taratuta
    The new bosonic mechanism Rostislav Taratuta To cite this version: Rostislav Taratuta. The new bosonic mechanism. 2016. hal-01162606v7 HAL Id: hal-01162606 https://hal.archives-ouvertes.fr/hal-01162606v7 Preprint submitted on 22 Sep 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution - NonCommercial - NoDerivatives| 4.0 International License The new bosonic mechanism. Rostislav A. Taratuta V.Ye. Lashkaryov Institute of Semiconductor Physics, Kiev, Ukraine corresponding author, email: r.tr@verizon.net ABSTRACT 1. Purpose The main purpose of this paper is to introduce the new bosonic mechanism and new treatment of dark energy. The bosonic mechanism focuses on obtaining masses by gauge bosons without assuming the existence of Higgs boson. This paper highlights the possibility for gauge boson to obtain mass not by means of interaction with Higgs boson, but by interacting with massive scalar mode of a single gravitational-dark field. The advantage of this approach over Higgs model is the manifest that the gauge boson acquires mass through interaction with combined gravitational dark field thus allowing the mechanism to account for the dark sector while Higgs model does not include dark sector.
    [Show full text]
  • Introductory Lectures on String Theory and the Ads/CFT Correspondence
    AEI-2002-034 Introductory Lectures on String Theory and the AdS/CFT Correspondence Ari Pankiewicz and Stefan Theisen 1 Max-Planck-Institut f¨ur Gravitationsphysik, Albert-Einstein-Institut, Am M¨uhlenberg 1,D-14476 Golm, Germany Summary: The first lecture is of a qualitative nature. We explain the concept and the uses of duality in string theory and field theory. The prospects to understand QCD, the theory of the strong interactions, via string theory are discussed and we mention the AdS/CFT correspondence. In the remaining three lectures we introduce some of the tools which are necessary to understand many (but not all) of the issues which were raised in the first lecture. In the second lecture we give an elementary introduction to string theory, concentrating on those aspects which are necessary for understanding the AdS/CFT correspondence. We present both open and closed strings, introduce D-branes and determine the spectra of the type II string theories in ten dimensions. In lecture three we discuss brane solutions of the low energy effective actions, the type II supergravity theories. In the final lecture we compare the two brane pictures – D-branes and supergravity branes. This leads to the formulation of the Maldacena conjecture, or the AdS/CFT correspondence. We also give a brief introduction to the conformal group and AdS space. 1Based on lectures given in July 2001 at the Universidad Simon Bolivar and at the Summer School on ”Geometric and Topological Methods for Quantum Field Theory” in Villa de Leyva, Colombia. Lecture 1: Introduction There are two central open problems in theoretical high energy physics: the search for a quantum theory of gravity and • the solution of QCD at low energies.
    [Show full text]
  • The Generation of Particles by Quantum Loops
    Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 21 May 2019 Article The generation of particles by quantum loops Hans Diel Diel Software Beratung und Entwicklung, Seestr.102, 71067 Sindelfingen, Germany, diel@netic.de Academic Editor: name Version May 21, 2019 submitted to Preprints 1 Abstract: Quantum loops are processes that constitute quantum objects. In the causal model of 2 quantum loops and quantum objects presented here, the nonlinear processes involve the elementary 3 units of spacetime and the associated elementary units of quantum fields. As such, quantum loop 4 processes are the sources of gravitational fields (i.e., spacetime curvature) and of the quantum objects 5 wave function. The model may be viewed as a derivative of loop quantum gravity, spin networks 6 and causal dynamical triangulation, although significant deviations to these theories exist. The causal 7 model of quantum loops is based on a causal model of spacetime dynamics where space(-time) 8 consists of interconnected space points, each of which is connected to a small number of neighboring 9 space points. The curvature of spacetime is expressed by the density of these space points and by the 10 arrangement of the connections between them. The quantum loop emerges in a nonlinear collective 11 behavioral process from a collection of space points that carry energy and quantum field attributes. 12 Keywords: spacetime models, causal models, nonlinear dynamics, relativity theory, quantum field 13 theory, quantum loops 14 1. Introduction 15 The author’s work on causal models of quantum theory (QT), quantum field theory (QFT) and 16 spacetime dynamics started with the attempt to develop a computer model of QT.
    [Show full text]
  • Consistency of the Standard Model Effective Field Theory
    Consistency of the Standard Model Effective Field Theory Grant N. Remmen and Nicholas L. Rodd Center for Theoretical Physics and Department of Physics University of California, Berkeley, CA 94720, USA and Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Abstract We derive bounds on couplings in the standard model effective field theory (SMEFT) as a consequence of causality and the analytic structure of scattering amplitudes. In the SMEFT, there are 64 independent operators at mass dimension eight that are quartic in bosons (either Higgs or gauge fields) and that contain four derivatives and/or field strengths, including both CP-conserving and CP-violating operators. Using analytic dispersion rela- tion arguments for two-to-two bosonic scattering amplitudes, we derive 27 independent bounds on the sign or magnitude of the couplings. We show that these bounds also follow as a consequence of causality of signal propagation in nonvacuum SM backgrounds. These bounds come in two qualitative forms: i) positivity of (various linear combinations of) cou- plings of CP-even operators and ii) upper bounds on the magnitude of CP-odd operators in terms of (products of) CP-even couplings. We exhibit various classes of example comple- tions, which all satisfy our EFT bounds. These bounds have consequences for current and arXiv:1908.09845v3 [hep-ph] 14 Sep 2020 future particle physics experiments, as part of the observable parameter space is inconsis- tent with causality and analyticity. To demonstrate the impact of our bounds, we consider applications both to SMEFT constraints derived at colliders and to limits on the neutron electric dipole moment, highlighting the connection between such searches suggested by infrared consistency.
    [Show full text]
  • Supersymmetry at 100
    There are two types of symmetries in momentum of a particle (remaining even at difference is clarified in the so-called spin- nature: external (or space-time) symmetries rest) is called spin. (Particle spin is an ex- statistics theorem that states that bosons and internal symmetries. Examples of inter- ternal symmetry, whereas isotopic spin, must satisfy commutation relations (the nal symmetries are the symmetry of isotopic which is not based on Lorentz invariance, is quantum mechanical wave function is sym- spin that identifies related energy levels of not.) metric under the interchange of identical the nucleons (protons and neutrons) and the In quantum mechanics spin comes in inte- bosons) and that fermions must satisfy a.nti- more encompassing SU(3) X SU(2) X U(1) gral or half-integral multiples of a fundamen- commutation relations (antisymmetnc wave symmetry of the standard model (see “Par- tal unit h (h = h/2z where h is Planck’s functions). The ramification of this simple ticle Physics and the Standard Model”). constant). (Orbital angular momentum only statement is that an indefinite number of Operations with these symmetries do not comes in integral multiples of h.) Particles bosons can exist in th~ same place at the change the space-time properties of a par- with integral values of spin (O, h, 273, . .) are same time, whereas only one fermion can be ticle. called bosons, and those with half-integral in any given place at a given time (Fig,, 1). External symmetries include translation spins (r5/2, 3fz/2, 5h/2, . .) are called fer- Hence “matter” (for example, atoms) is invariance and invariance under the Lorentz miens.
    [Show full text]
  • Phase-Factor-Dependent Symmetries and Quantum Phases in a Three
    www.nature.com/scientificreports OPEN Phase-factor-dependent symmetries and quantum phases in a three-level cavity QED system Received: 08 December 2015 Jingtao Fan1,2, Lixian Yu3, Gang Chen1,2 & Suotang Jia1,2 Accepted: 12 April 2016 Unlike conventional two-level particles, three-level particles may support some unitary-invariant Published: 03 May 2016 phase factors when they interact coherently with a single-mode quantized light field. To gain a better understanding of light-matter interaction, it is thus necessary to explore the phase-factor-dependent physics in such a system. In this report, we consider the collective interaction between degenerate V-type three-level particles and a single-mode quantized light field, whose different components are labeled by different phase factors. We mainly establish an important relation between the phase factors and the symmetry or symmetry-broken physics. Specifically, we find that the phase factors affect dramatically the system symmetry. When these symmetries are breaking separately, rich quantum phases emerge. Finally, we propose a possible scheme to experimentally probe the predicted physics of our model. Our work provides a way to explore phase-factor-induced nontrivial physics by introducing additional particle levels. Symmetry and spontaneous symmetry breaking are central concepts in modern many-body physics1–3, due to their natural and clear relations with quantum phase transitions4. It is the emergence of a new phase that breaks an intrinsic symmetry of the system. More importantly, different symmetry-broken phases usually exhibit dif- ferent ground-state properties. As a fundamental model of many-body physics, the Dicke model describes the collective interaction between two-level particles (such as atoms, molecules, and superconducting qubits, etc.) 5 and a single-mode quantized light field .
    [Show full text]
  • Dynamical Boson Stars
    Dynamical Boson Stars Steven L. Liebling Long Island University Brookville, NY 11548 USA email: steve.liebling@liu.edu http://relativity.liu.edu/steve Carlos Palenzuela Universitat de les Illes Balears Palma de Mallorca, 07122 Baleares, Spain email: carlos.palenzuela@uib.es http://www.grg.uib.es/index.php Contents 1 Introduction 3 1.1 The nature of a boson star . 4 1.2 Other reviews . 5 2 Solving for Boson Stars 7 2.1 Conventions . 7 2.2 The Lagrangian, evolution equations and conserved quantities . 7 2.3 The 3+1 decomposition of the spacetime . 8 2.4 Mini-boson stars . 10 3 Varieties of Boson Stars 13 3.1 Self-interaction potentials . 13 3.2 Newtonian boson stars . 16 3.3 Charged boson stars . 17 3.4 Oscillatons . 19 3.5 Rotating boson stars . 21 arXiv:1202.5809v3 [gr-qc] 23 May 2017 3.6 Fermion-boson stars . 22 3.7 Multi-state boson stars . 24 3.8 Proca stars . 26 3.9 Kerr black holes with scalar hair & superradiance . 28 3.10 Alternative theories of gravity . 29 3.11 Gauged boson stars . 30 4 Dynamics of Boson Stars 31 4.1 Gravitational stability . 31 4.1.1 Linear stability analysis . 31 4.1.2 Non-linear stability of single boson stars . 33 4.2 Dynamics of binary boson stars . 37 1 5 Boson Stars in Astronomy 42 5.1 As astrophysical stellar objects . 42 5.2 Compact alternatives to black holes . 45 5.3 As source of gravitational waves . 47 5.4 As origin of dark matter . 48 6 Boson Stars in Mathematical Relativity 50 6.1 Black hole critical behavior .
    [Show full text]