Relevance of the eigenstate thermalization hypothesis for thermal relaxation
arXiv:1408.0187 · doi:10.1103/PhysRevE.91.012120
Abstract
We study the validity of the eigenstate thermalization hypothesis (ETH) and its role for the occurrence of initial-state independent (ISI) equilibration in closed quantum many-body systems. Using the concept of dynamical typicality, we present an extensive numerical analysis of energy exchange in integrable and nonintegrable spin-1/2 systems of large size outside the range of exact diagonalization. In case of nonintegrable systems, our finite-size scaling shows that the ETH becomes valid in the thermodynamic limit and can serve as the underlying mechanism for ISI equilibration. In case of integrable systems, however, indication of ISI equilibration has been observed despite the violation of the ETH. We establish a connection between this observation and the need of choosing a proper parameter within the ETH.
arXiv comment6 pages, 5 figures
References in corpus (35)
- Many-Body Physics with Ultracold Gases
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
- The many-body localization phase transition
- Light-cone-like spreading of correlations in a quantum many-body system
- Non-equilibrium coherence dynamics in one-dimensional Bose gases
- Canonical Typicality
- Time-resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices
- Quantum mechanical evolution towards thermal equilibrium
- Breakdown of thermalization in finite one-dimensional systems
- Foundation of Statistical Mechanics under experimentally realistic conditions
- Local emergence of thermal correlations in an isolated quantum many-body system
- Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems
- Alternatives to Eigenstate Thermalization
- Absence of Thermalization in Nonintegrable Systems
- Finite-size scaling of eigenstate thermalization
- Effective thermal dynamics following a quantum quench in a spin chain
- Hard-core bosons on optical superlattices: Dynamics and relaxation in the superfluid and insulating regimes
- Massive Parallel Quantum Computer Simulator
- Thermalization in Nature and on a Quantum Computer
- Eigenstate thermalization within isolated spin-chain systems
- Dynamical typicality of quantum expectation values
- Pushing the limits of the eigenstate thermalization hypothesis towards mesoscopic quantum systems
- Spin-current autocorrelations from single pure-state propagation
- Chaos and statistical relaxation in quantum systems of interacting particles
- Finite-Size Scaling Analysis of the Eigenstate Thermalization Hypothesis in a One-Dimensional Interacting Bose gas
- Regression relation for pure quantum states and its implications for efficient computing
- Long-time behavior of many-particle quantum decay
- Eigenstate Randomization Hypothesis: Why Does the Long-Time Average Equal the Microcanonical Average?
- Memory of the Initial Conditions in an Incompletely-Chaotic Quantum System: Universal Predictions and an Application to Cold Atoms
- Computational Methods for Simulating Quantum Computers
- Initial state dependence of the quench dynamics in integrable quantum systems. III. Chaotic states
- A necessary condition for the thermalization of a quantum system coupled to a quantum bath
- Relaxation to equilibrium of expectation values in macroscopic quantum systems
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- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Thermalization and prethermalization in isolated quantum systems: a theoretical overview
- Off-diagonal matrix elements of local operators in many-body quantum systems
- Nonthermal states arising from confinement in one and two dimensions
- Eigenstate thermalization in the two-dimensional transverse field Ising model: II. Off-diagonal matrix elements of observables
- Signatures of rare states and thermalization in a theory with confinement
- Eigenstate thermalization and quantum chaos in the Holstein polaron model
- Equilibration time scales of physically relevant observables
- Eigenstate thermalization hypothesis and integrals of motion
- Numerical Large Deviation Analysis of Eigenstate Thermalization Hypothesis
- Emergence of Hilbert Space Fragmentation in Ising Models with a Weak Transverse Field
- Thermalization and Heating Dynamics in Open Generic Many-Body Systems
- Generalized Gibbs ensemble in a nonintegrable system with an extensive number of local symmetries
- Why are macroscopic experiments reproducible? Imitating the behavior of an ensemble by single pure states
- Degenerate observables and the many Eigenstate Thermalization Hypotheses
- How accurately can the microcanonical ensemble describe small isolated quantum systems?
- Information-theoretic equilibrium and observable thermalization
- Statistical mechanics for non-Hermitian quantum systems
- Hydrodynamics and the eigenstate thermalization hypothesis
- Hologram of a pure state black hole
- Noncommutative generalized Gibbs ensemble in isolated integrable quantum systems
- Characterization of random features of chaotic eigenfunctions in unperturbed basis
- Random-matrix behavior of quantum nonintegrable many-body systems with Dyson's three symmetries
- Work Extraction from a Single Energy Eigenstate
- Necessity of eigenstate thermalization for equilibration towards unique expectation values when starting from generic initial states
- Stiffness of Probability Distributions of Work and Jarzynski Relation for Non-Gibbsian Initial States
- Generalized eigenstate typicality in translation-invariant quasifree fermionic models
- Eigenstate thermalization scaling in approaching the classical limit
- Continuous-time quantum walks for MAX-CUT are hot
- Deep reinforcement learning for preparation of thermal and prethermal quantum states
- Classical route to ergodicity and scarring in collective quantum systems
- Exploring integrability-chaos transition with a sequence of independent perturbations
- Relaxation of dynamically prepared out-of-equilibrium initial states within and beyond linear response theory
- Relaxation dynamics of ultracold bosons in a double-well potential: Thermalization and prethermalization in a nearly integrable model
- Statistical distribution of components of energy eigenfunctions: from nearly-integrable to chaotic
- Microstate Distinguishability, Quantum Complexity, and the Eigenstate Thermalization Hypothesis
- The second law of thermodynamics from concavity of energy eigenvalues
- Initial State Independent Equilibration at the Breakdown of the Eigenstate Thermalization Hypothesis
- Key Observable for Linear Thermalization
- Continuous-time quantum optimisation without the adiabatic principle
- Hilbert space average of transition probabilities
- Macroscopic Thermalization for Highly Degenerate Hamiltonians After Slight Perturbation
- Macroproperties vs. Microstates in the Classical Simulation of Critical Phenomena in Quench Dynamics of 1D Ising Models
- Kinetically constrained models constructed from dissipative quantum dynamics
- Roles of energy eigenstates and eigenvalues in equilibration of isolated quantum systems
- Classical periodic trajectories and quantum scars in many-spin systems
- Quantum chaos in a harmonic waveguide with scatterers
- The second law of thermodynamics from concave energy in classical mechanics
- Eigenstate Thermalization Hypothesis and Random Matrix Theory Universality in Few-Body Systems
- Basis dependence of eigenstate thermalization
- On the difference between thermalization in open and isolated quantum systems: a case study
- Pure states statistical mechanics: On its foundations and applications to quantum gravity