Semiclassical proof of the many-body eigenstate thermalization
hypothesis
- URL: http://arxiv.org/abs/2210.13183v1
- Date: Fri, 21 Oct 2022 01:39:54 GMT
- Title: Semiclassical proof of the many-body eigenstate thermalization
hypothesis
- Authors: Wen-ge Wang
- Abstract summary: The eigenstate thermalization hypothesis (ETH) supplies a way of understanding eventual thermalization.
However, an analytical proof of ETH is still lacking.
In this Letter, the ETH ansatz is demonstrated for an arbitrary observable of an arbitrary subsystem in a generic many-body quantum chaotic system.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The so-called eigenstate thermalization hypothesis (ETH), which has been
tested in various models by numerical simulations, supplies a way of
understanding eventual thermalization and is believed to be important for
understanding processes of thermalization. However, an analytical proof of ETH
is still lacking. In this Letter, the ETH ansatz is demonstrated for an
arbitrary observable of an arbitrary subsystem in a generic many-body quantum
chaotic system, to which the so-called Berry's conjecture is applicable. In
particular, semiclassical expressions are derived for two unknown functions in
the ETH ansatz.
Related papers
- Quantum Fisher Information for Different States and Processes in Quantum
Chaotic Systems [77.34726150561087]
We compute the quantum Fisher information (QFI) for both an energy eigenstate and a thermal density matrix.
We compare our results with earlier results for a local unitary transformation.
arXiv Detail & Related papers (2023-04-04T09:28:19Z) - Non-Hermitian Hamiltonians Violate the Eigenstate Thermalization
Hypothesis [0.0]
Eigenstate Thermalization Hypothesis (ETH) represents a cornerstone in the theoretical understanding of the emergence of thermal behavior in closed quantum systems.
We investigate what extent the ETH holds in non-Hermitian many-body systems.
We come to the surprising conclusion that the fluctuations between eigenstates is of equal order to the average, indicating no thermalization.
arXiv Detail & Related papers (2023-03-06T19:17:15Z) - Thermalization without eigenstate thermalization [7.88657961743755]
We study the thermalization of a subsystem in an isolated quantum many-body system.
In this setting, the eigenstate thermalization hypothesis (ETH) was proposed to explain thermalization.
arXiv Detail & Related papers (2022-09-20T16:16:17Z) - Non-Abelian eigenstate thermalization hypothesis [58.720142291102135]
The eigenstate thermalization hypothesis (ETH) explains why chaotic quantum many-body systems thermalize internally if the Hamiltonian lacks symmetries.
We adapt the ETH to noncommuting charges by positing a non-Abelian ETH and invoking the approximate microcanonical subspace introduced in quantum thermodynamics.
arXiv Detail & Related papers (2022-06-10T18:14:18Z) - Thermalization of locally perturbed many-body quantum systems [0.0]
We analytically demonstrate that systems satisfying the weak eigenstate thermalization hypothesis exhibit thermalization for two very natural classes of far-from-equilibrium initial conditions.
arXiv Detail & Related papers (2022-02-01T08:16:05Z) - Fast Thermalization from the Eigenstate Thermalization Hypothesis [69.68937033275746]
Eigenstate Thermalization Hypothesis (ETH) has played a major role in understanding thermodynamic phenomena in closed quantum systems.
This paper establishes a rigorous link between ETH and fast thermalization to the global Gibbs state.
Our results explain finite-time thermalization in chaotic open quantum systems.
arXiv Detail & Related papers (2021-12-14T18:48:31Z) - On eigenstate thermalization in the SYK chain model [0.0]
Eigenstate thermalization hypothesis (ETH) explains how generic observables of individual isolated quantum systems in pure states can exhibit thermal behaviors.
We show that for two conventional few-body operators, the ensemble-averaged theory of the SYK chain model strictly satisfies ETH conditions.
arXiv Detail & Related papers (2021-04-12T08:50:24Z) - Taking the temperature of a pure quantum state [55.41644538483948]
Temperature is a deceptively simple concept that still raises deep questions at the forefront of quantum physics research.
We propose a scheme to measure the temperature of such pure states through quantum interference.
arXiv Detail & Related papers (2021-03-30T18:18:37Z) - Out-of-time-order correlations and the fine structure of eigenstate
thermalisation [58.720142291102135]
Out-of-time-orderors (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalisation.
We show explicitly that the OTOC is indeed a precise tool to explore the fine details of the Eigenstate Thermalisation Hypothesis (ETH)
We provide an estimation of the finite-size scaling of $omega_textrmGOE$ for the general class of observables composed of sums of local operators in the infinite-temperature regime.
arXiv Detail & Related papers (2021-03-01T17:51:46Z) - Probing eigenstate thermalization in quantum simulators via
fluctuation-dissipation relations [77.34726150561087]
The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems.
Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations.
Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
arXiv Detail & Related papers (2020-07-20T18:00:02Z) - Does the Eigenstate Thermalization Hypothesis Imply Thermalization? [0.0]
Eigenstate thermalization hypothesis (ETH) is discussed.
We show that one common formulation of ETH does not necessarily imply thermalization of an observable of isolated many body quantum system.
arXiv Detail & Related papers (2020-02-05T16:38:20Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.