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Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport

Reports on Progress in Physics, ISSN 0034-4885, 11/2011, Volume 74, Issue 11, pp. 116601 - 41

Unlike equilibrium statistical mechanics, with its well-established foundations, a similar widely accepted framework for non-equilibrium statistical mechanics...

ASYMMETRIC XXZ CHAIN | PHYSICS, MULTIDISCIPLINARY | FIELD-THEORY | RENORMALIZATION-GROUP METHODS | SINGLE-FILE DIFFUSION | PARISI-ZHANG EQUATION | SIMPLE EXCLUSION PROCESS | FREE-ENERGY | DRIVEN DIFFUSIVE SYSTEMS | BETHE-ANSATZ SOLUTION | FLUCTUATION-DISSIPATION THEOREM | Cellular | Dynamics | Mathematical analysis | Ingredients | Mathematical models | Statistical mechanics | Transport | Dynamical systems

ASYMMETRIC XXZ CHAIN | PHYSICS, MULTIDISCIPLINARY | FIELD-THEORY | RENORMALIZATION-GROUP METHODS | SINGLE-FILE DIFFUSION | PARISI-ZHANG EQUATION | SIMPLE EXCLUSION PROCESS | FREE-ENERGY | DRIVEN DIFFUSIVE SYSTEMS | BETHE-ANSATZ SOLUTION | FLUCTUATION-DISSIPATION THEOREM | Cellular | Dynamics | Mathematical analysis | Ingredients | Mathematical models | Statistical mechanics | Transport | Dynamical systems

Journal Article

Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, 10/2014, Volume 2014, Issue 10, pp. P10035 - 53

We consider the time evolution in the repulsive sine-Gordon quantum field theory after the system is prepared in a particular class of initial states. We focus...

Integrable quantum field theory | Correlation functions | Quantum quenches | Form factors | integrable quantum field theory | COPPER BENZOATE | XXZ SPIN CHAIN | FIELD-THEORY | quantum quenches | RELAXATION | PHYSICS, MATHEMATICAL | correlation functions | FINITE-VOLUME | form factors | MECHANICS | BOUNDARY STATE | DIMENSIONAL S=1/2 ANTIFERROMAGNET | ISING-MODEL | CU BENZOATE | EXACT FORM-FACTORS | Time dependence | Operators | Correlation | Decay rate | Mathematical analysis | Evolution | Mathematical models | Statistical mechanics | Physics - Statistical Mechanics

Integrable quantum field theory | Correlation functions | Quantum quenches | Form factors | integrable quantum field theory | COPPER BENZOATE | XXZ SPIN CHAIN | FIELD-THEORY | quantum quenches | RELAXATION | PHYSICS, MATHEMATICAL | correlation functions | FINITE-VOLUME | form factors | MECHANICS | BOUNDARY STATE | DIMENSIONAL S=1/2 ANTIFERROMAGNET | ISING-MODEL | CU BENZOATE | EXACT FORM-FACTORS | Time dependence | Operators | Correlation | Decay rate | Mathematical analysis | Evolution | Mathematical models | Statistical mechanics | Physics - Statistical Mechanics

Journal Article

Physical Review Letters, ISSN 0031-9007, 07/2017, Volume 119, Issue 2, p. 020602

Nonergodic dynamical systems display anomalous transport properties. Prominent examples are integrable quantum systems, whose exceptional properties are...

Physics and Astronomy(all) | DIMENSIONAL HUBBARD-MODEL | SPIN-1/2 XXZ CHAIN | TRANSPORT-PROPERTIES | THERMODYNAMICS | PHYSICS, MULTIDISCIPLINARY | THERMAL-CONDUCTIVITY | CHARGE STIFFNESS | DRUDE WEIGHT | HEISENBERG-MODEL | BETHE-ANSATZ

Physics and Astronomy(all) | DIMENSIONAL HUBBARD-MODEL | SPIN-1/2 XXZ CHAIN | TRANSPORT-PROPERTIES | THERMODYNAMICS | PHYSICS, MULTIDISCIPLINARY | THERMAL-CONDUCTIVITY | CHARGE STIFFNESS | DRUDE WEIGHT | HEISENBERG-MODEL | BETHE-ANSATZ

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 08/2016, Volume 49, Issue 35, p. 354001

In this paper and its sequel, we construct topologically invariant defects in two-dimensional classical lattice models and quantum spin chains. We show how...

fusion category | Ising model | topological defects | Krammers-Wannier duality | IDENTITIES | PHYSICS, MULTIDISCIPLINARY | SPIN-1/2 XXZ | TFT CONSTRUCTION | TWISTED BOUNDARY-CONDITIONS | PHYSICS, MATHEMATICAL | SYMMETRY | CONFORMAL FIELD-THEORY | DUALITY | SYSTEMS | SPECTRUM | SURFACES

fusion category | Ising model | topological defects | Krammers-Wannier duality | IDENTITIES | PHYSICS, MULTIDISCIPLINARY | SPIN-1/2 XXZ | TFT CONSTRUCTION | TWISTED BOUNDARY-CONDITIONS | PHYSICS, MATHEMATICAL | SYMMETRY | CONFORMAL FIELD-THEORY | DUALITY | SYSTEMS | SPECTRUM | SURFACES

Journal Article

Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, 06/2016, Volume 2016, Issue 6, p. 63101

We present an identification of the spectra of local conserved operators of integrable quantum lattice models and the density distributions of their...

algebraic structures of integrable models | quantum quenches | quantum integrability (Bethe Ansatz) | symmetries of integrable models | MANY-BODY SYSTEM | LOCAL CONSERVATION-LAWS | PHYSICS, MATHEMATICAL | FUNCTIONAL RELATIONS | SPIN-1/2 | XXZ CHAIN | MECHANICS | CONFORMAL FIELD-THEORY | Q-OPERATOR | QUANTUM-SYSTEMS | FINITE-TEMPERATURE | HEISENBERG-MODEL

algebraic structures of integrable models | quantum quenches | quantum integrability (Bethe Ansatz) | symmetries of integrable models | MANY-BODY SYSTEM | LOCAL CONSERVATION-LAWS | PHYSICS, MATHEMATICAL | FUNCTIONAL RELATIONS | SPIN-1/2 | XXZ CHAIN | MECHANICS | CONFORMAL FIELD-THEORY | Q-OPERATOR | QUANTUM-SYSTEMS | FINITE-TEMPERATURE | HEISENBERG-MODEL

Journal Article

Nuclear Physics, Section B, ISSN 0550-3213, 04/2014, Volume 881, Issue 1, pp. 343 - 368

We study integrable models solvable by the nested algebraic Bethe ansatz and possessing GL(3)-invariant R-matrix. We obtain determinant representations for...

Form factors | Nested algebraic Bethe ansatz | Nested algebraic bethe ansatz | CHAIN | SINE-GORDON MODEL | WAVE-FUNCTIONS | FIELD-THEORIES | REGIME | XXZ MODEL | OPERATORS | EQUATION | PHYSICS, PARTICLES & FIELDS | Mathematical Physics | Nuclear and High Energy Physics

Form factors | Nested algebraic Bethe ansatz | Nested algebraic bethe ansatz | CHAIN | SINE-GORDON MODEL | WAVE-FUNCTIONS | FIELD-THEORIES | REGIME | XXZ MODEL | OPERATORS | EQUATION | PHYSICS, PARTICLES & FIELDS | Mathematical Physics | Nuclear and High Energy Physics

Journal Article

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Lattice approach to finite volume form-factors of the Massive Thirring (Sine-Gordon) model

Journal of High Energy Physics, ISSN 1126-6708, 8/2017, Volume 2017, Issue 8, pp. 1 - 31

In this paper we demonstrate, that the light-cone lattice approach for the Massive-Thirring (sine-Gordon) model, through the quantum inverse scattering method,...

Lattice Integrable Models | Integrable Field Theories | Quantum Physics | Bethe Ansatz | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | DYNAMICAL CORRELATION-FUNCTIONS | NONLINEAR INTEGRAL-EQUATION | BETHE-ANSATZ | EXCITED-STATES | XXZ CHAIN | SPIN CORRELATION-FUNCTIONS | MAGNETIC-FIELD | QFT | SCALING FUNCTIONS | PHYSICS, PARTICLES & FIELDS | Thermodynamics | Analysis | Models | Operators | Uranium | Inverse scattering | Elastic scattering

Lattice Integrable Models | Integrable Field Theories | Quantum Physics | Bethe Ansatz | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | DYNAMICAL CORRELATION-FUNCTIONS | NONLINEAR INTEGRAL-EQUATION | BETHE-ANSATZ | EXCITED-STATES | XXZ CHAIN | SPIN CORRELATION-FUNCTIONS | MAGNETIC-FIELD | QFT | SCALING FUNCTIONS | PHYSICS, PARTICLES & FIELDS | Thermodynamics | Analysis | Models | Operators | Uranium | Inverse scattering | Elastic scattering

Journal Article

Journal of Magnetism and Magnetic Materials, ISSN 0304-8853, 04/2018, Volume 452, pp. 315 - 320

•The phase diagram at zero temperature is obtained.•The SU(3) Schwinger bosons formalism is used.•The Kosterlitz-Thouless transition temperature is calculated...

Antiferromagnet | Quantum phase transition | Frustrated systems | PHYSICS, CONDENSED MATTER | QUANTUM | MATERIALS SCIENCE, MULTIDISCIPLINARY | SINGLE-ION-ANISOTROPY | STIFFNESS | 2-DIMENSIONAL XXZ MODEL | PLANE | DYNAMICS | CONSISTENT HARMONIC APPROXIMATION | HEISENBERG-ANTIFERROMAGNET

Antiferromagnet | Quantum phase transition | Frustrated systems | PHYSICS, CONDENSED MATTER | QUANTUM | MATERIALS SCIENCE, MULTIDISCIPLINARY | SINGLE-ION-ANISOTROPY | STIFFNESS | 2-DIMENSIONAL XXZ MODEL | PLANE | DYNAMICS | CONSISTENT HARMONIC APPROXIMATION | HEISENBERG-ANTIFERROMAGNET

Journal Article

Physical Review Letters, ISSN 0031-9007, 09/2016, Volume 117, Issue 11, p. 116401

We study the thermal conductivity of the one-dimensional Fermi-Hubbard model at a finite temperature using a density matrix renormalization group approach. The...

XXZ CHAIN | STATISTICAL-MECHANICAL THEORY | TRANSPORT | IRREVERSIBLE PROCESSES | OPTICAL LATTICE | ULTRACOLD ATOMS | PHYSICS, MULTIDISCIPLINARY | MOTT INSULATOR | PRODUCT STATES | CARBON NANOTUBES | DENSITY-MATRIX RENORMALIZATION | Temperature dependence | Mathematical analysis | Thermal conductivity | Spreads | Transport | Energy transfer | Density | Heat transfer

XXZ CHAIN | STATISTICAL-MECHANICAL THEORY | TRANSPORT | IRREVERSIBLE PROCESSES | OPTICAL LATTICE | ULTRACOLD ATOMS | PHYSICS, MULTIDISCIPLINARY | MOTT INSULATOR | PRODUCT STATES | CARBON NANOTUBES | DENSITY-MATRIX RENORMALIZATION | Temperature dependence | Mathematical analysis | Thermal conductivity | Spreads | Transport | Energy transfer | Density | Heat transfer

Journal Article

Nuclear Physics, Section B, ISSN 0550-3213, 04/2015, Volume 893, pp. 305 - 331

Following Sklyanin's proposal in the periodic case, we derive the generating function of the Gaudin Hamiltonians with boundary terms. Our derivation is based...

CHAIN | MAGNET | XXZ-SPIN | EQUATION | PHYSICS, PARTICLES & FIELDS | Exactly Solvable and Integrable Systems | Nonlinear Sciences | Mathematical Physics | Nuclear and High Energy Physics | Nuclear and particle physics. Atomic energy. Radioactivity | Terms | Spin chains | Magnets | High Energy Physics - Theory | Systems | Nonlinear Sciences - Exactly Solvable and Integrable Systems | Xxz spin | [ NLIN.NLIN-SI ] Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI] | Knizhnik zamolodchikov equation

CHAIN | MAGNET | XXZ-SPIN | EQUATION | PHYSICS, PARTICLES & FIELDS | Exactly Solvable and Integrable Systems | Nonlinear Sciences | Mathematical Physics | Nuclear and High Energy Physics | Nuclear and particle physics. Atomic energy. Radioactivity | Terms | Spin chains | Magnets | High Energy Physics - Theory | Systems | Nonlinear Sciences - Exactly Solvable and Integrable Systems | Xxz spin | [ NLIN.NLIN-SI ] Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI] | Knizhnik zamolodchikov equation

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 01/2018, Volume 51, Issue 1, p. 1

We examine many-body localization properties for the eigenstates that lie in the droplet sector of the random-field spin-1/2 XXZ chain. These states satisfy a...

Lieb-Robinson bound | exponential clustering | XXZ spin chain in a random field | many-body localization | TRANSITION | SYSTEM | STATES | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL

Lieb-Robinson bound | exponential clustering | XXZ spin chain in a random field | many-body localization | TRANSITION | SYSTEM | STATES | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 11/2013, Volume 46, Issue 45, pp. 1 - 13

We consider a formulation of the algebraic Bethe ansatz for the six vertex model with non-diagonal open boundaries. Specifically, we study the case where both...

KNIZHNIK-ZAMOLODCHIKOV EQUATION | XXZ SPIN CHAIN | PHYSICS, MULTIDISCIPLINARY | GAUDIN MAGNET | SYSTEMS | PHYSICS, MATHEMATICAL | FUNCTIONAL RELATIONS | OPEN BOUNDARY-CONDITIONS | Operators | Construction | Mathematical models | Algebra | Boundaries | Excitation

KNIZHNIK-ZAMOLODCHIKOV EQUATION | XXZ SPIN CHAIN | PHYSICS, MULTIDISCIPLINARY | GAUDIN MAGNET | SYSTEMS | PHYSICS, MATHEMATICAL | FUNCTIONAL RELATIONS | OPEN BOUNDARY-CONDITIONS | Operators | Construction | Mathematical models | Algebra | Boundaries | Excitation

Journal Article

Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, 07/2015, Volume 2015, Issue 7, pp. P07007 - 13

We show a correspondence of all the solutions of the Bethe ansatz equations of the one-dimensional spin-1/2 isotropic Heisenberg model with periodic boundary...

integrable spin chains (vertex models) | quantum integrability (Bethe Ansatz) | BETHE-ANSATZ EQUATIONS | STATES | MECHANICS | STRING HYPOTHESIS | UNITY | SPIN CHAIN | XXZ MODEL | ROOTS | PHYSICS, MATHEMATICAL | Quantum numbers | Mathematical analysis | Boundary conditions | Mathematical models | Mapping | Statistical mechanics | Rigging

integrable spin chains (vertex models) | quantum integrability (Bethe Ansatz) | BETHE-ANSATZ EQUATIONS | STATES | MECHANICS | STRING HYPOTHESIS | UNITY | SPIN CHAIN | XXZ MODEL | ROOTS | PHYSICS, MATHEMATICAL | Quantum numbers | Mathematical analysis | Boundary conditions | Mathematical models | Mapping | Statistical mechanics | Rigging

Journal Article

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, ISSN 1742-5468, 07/2019, Volume 2019, Issue 7, p. 74003

We establish the exact laws of large numbers for two time additive quantities in the raise and peel model, the number of tiles removed by avalanches and the...

solvable lattice models | MECHANICS | XXZ SPIN CHAIN | GROUND-STATE | DELTA=-1/2 | growth processes | integrable spin chains and vertex models | large deviations in non-equilibrium systems | PHYSICS, MATHEMATICAL | O LOOP MODEL

solvable lattice models | MECHANICS | XXZ SPIN CHAIN | GROUND-STATE | DELTA=-1/2 | growth processes | integrable spin chains and vertex models | large deviations in non-equilibrium systems | PHYSICS, MATHEMATICAL | O LOOP MODEL

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 02/2018, Volume 491, pp. 604 - 612

A quantum Otto heat engine is established with a three-qubit Heisenberg XXZ model with Dzyaloshinskii–Moriya (DM) interaction under a homogeneous magnetic...

Quantum Otto heat engine | Heisenberg [formula omitted] model | Heisenberg XXZ model | SUPERCONDUCTING CIRCUITS | MAXWELLS DEMON | ATOMIC PHYSICS | PHYSICS, MULTIDISCIPLINARY | Magnetic fields | Anisotropy | Analysis

Quantum Otto heat engine | Heisenberg [formula omitted] model | Heisenberg XXZ model | SUPERCONDUCTING CIRCUITS | MAXWELLS DEMON | ATOMIC PHYSICS | PHYSICS, MULTIDISCIPLINARY | Magnetic fields | Anisotropy | Analysis

Journal Article

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Signatures of non-Abelian anyons in the thermodynamics of an interacting fermion model

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 04/2018, Volume 51, Issue 19, p. 195001

The contribution of anyonic degrees of freedom emerging in the non-Abelian spin sector of a one-dimensional system of interacting fermions carrying both SU(2)...

Bethe ansatz | anyons | parafermions | quantum phase transitions | GROUND-STATE | PHYSICS, MULTIDISCIPLINARY | ARBITRARY SPIN | PHYSICS, MATHEMATICAL | XXZ HEISENBERG-MODEL | BOSONS | Physics - Strongly Correlated Electrons

Bethe ansatz | anyons | parafermions | quantum phase transitions | GROUND-STATE | PHYSICS, MULTIDISCIPLINARY | ARBITRARY SPIN | PHYSICS, MATHEMATICAL | XXZ HEISENBERG-MODEL | BOSONS | Physics - Strongly Correlated Electrons

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 6/2014, Volume 2014, Issue 6, pp. 1 - 22

The Izergin-Korepin model with general non-diagonal boundary terms, a typical integrable model beyond A-type and without U(1)-symmetry, is studied via the...

Lattice Integrable Models | Quantum Physics | Bethe Ansatz | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | INVERSE SCATTERING METHOD | XXZ SPIN CHAIN | T-Q RELATION | ALGEBRA | FUNCTIONAL RELATIONS | VERTEX MODEL | VARIABLES | QUANTUM CHAIN | SEPARATION | BETHE-ANSATZ SOLUTION | PHYSICS, PARTICLES & FIELDS | Operators | Asymptotic properties | Mathematical analysis | Exact solutions | Mathematical models | Spectra | Boundaries | Product differentiation | Mathematical Physics | Nuclear and High Energy Physics | Condensed Matter - Statistical Mechanics | Nonlinear Sciences | Exactly Solvable and Integrable Systems | High Energy Physics - Theory

Lattice Integrable Models | Quantum Physics | Bethe Ansatz | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | INVERSE SCATTERING METHOD | XXZ SPIN CHAIN | T-Q RELATION | ALGEBRA | FUNCTIONAL RELATIONS | VERTEX MODEL | VARIABLES | QUANTUM CHAIN | SEPARATION | BETHE-ANSATZ SOLUTION | PHYSICS, PARTICLES & FIELDS | Operators | Asymptotic properties | Mathematical analysis | Exact solutions | Mathematical models | Spectra | Boundaries | Product differentiation | Mathematical Physics | Nuclear and High Energy Physics | Condensed Matter - Statistical Mechanics | Nonlinear Sciences | Exactly Solvable and Integrable Systems | High Energy Physics - Theory

Journal Article