# Alternatives to eigenstate thermalization.

@article{Rigol2012AlternativesTE, title={Alternatives to eigenstate thermalization.}, author={Marcos Rigol and Mark Allen Srednicki}, journal={Physical review letters}, year={2012}, volume={108 11}, pages={ 110601 } }

An isolated quantum many-body system in an initial pure state will come to thermal equilibrium if it satisfies the eigenstate thermalization hypothesis (ETH). We consider alternatives to ETH that have been proposed. We first show that von Neumann's quantum ergodic theorem relies on an assumption that is essentially equivalent to ETH. We also investigate whether, following a sudden quench, special classes of pure states can lead to thermal behavior in systems that do not obey ETH, namely…

## 29 Citations

On the Thermalization Hypothesis of Quantum States

- PhysicsProceedings of the Steklov Institute of Mathematics
- 2021

Abstract The eigenstate thermalization hypothesis (ETH) is discussed. We note that one common formulation of the ETH does not necessarily imply thermalization of an observable of an isolated…

Thermalization of isolated quantum many-body system and entanglement

- Physics
- 2020

Thermalization of an isolated quantum system has been a non-trivial problem since the early days of quantum mechanics. In generic isolated systems, non-equilibrium dynamics is expected to result in…

Does the Eigenstate Thermalization Hypothesis Imply Thermalization

- Physics
- 2020

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. To…

Dynamical Typicality Approach to Eigenstate Thermalization.

- PhysicsPhysical review letters
- 2018

It is shown by means of a dynamical typicality approach that most initial states within a microcanonical energy shell of an isolated many-body quantum system exhibit thermalization if and only if A satisfies the so-called weak eigenstate thermalization hypothesis (wETH).

Quantum thermalization and equilibrium state with multiple temperatures

- Physics
- 2014

A large class of isolated quantum systems in a pure state can equilibrate and serve as a heat bath. We show that, once equilibrium is reached, any of its subsystems, which are much smaller than the…

Pushing the limits of the eigenstate thermalization hypothesis towards mesoscopic quantum systems.

- PhysicsPhysical review letters
- 2014

This Letter presents an approach that pushes this limit up to system sizes of roughly 35 spins, thereby going significantly beyond what is possible with exact diagonalization.

Signatures of rare states and thermalization in a theory with confinement

- PhysicsPhysical Review B
- 2019

There is a dichotomy in the nonequilibrium dynamics of quantum many-body systems. In the presence of integrability, expectation values of local operators equilibrate to values described by a…

Generalization of von Neumann's Approach to Thermalization.

- PhysicsPhysical review letters
- 2015

Thermalization of isolated many-body systems is demonstrated by generalizing an approach originally due to von Neumann: For arbitrary initial states with a macroscopically well-defined energy,…

Eigenstate Thermalization for Degenerate Observables.

- PhysicsPhysical review letters
- 2018

It is shown that the relative overlaps are unbiased for highly degenerate observables and demonstrated that unless relative phases conspire to cumulative effects, this makes such observables verify the ETH.

Equilibration of isolated macroscopic quantum systems under experimentally realistic conditions

- Physics
- 2012

In how far does a non-equilibrium initial ensemble evolve towards a stationary long time behavior for an isolated macroscopic quantum system? We demonstrate that deviations from a steady state indeed…