# Impact of eigenstate thermalization on the route to equilibrium.

@article{Richter2019ImpactOE, title={Impact of eigenstate thermalization on the route to equilibrium.}, author={Jonas Richter and Jochen Gemmer and Robin Steinigeweg}, journal={Physical review. E}, year={2019}, volume={99 5-1}, pages={ 050104 } }

The eigenstate thermalization hypothesis (ETH) and the theory of linear response (LRT) are celebrated cornerstones of our understanding of the physics of many-body quantum systems out of equilibrium. While the ETH provides a generic mechanism of thermalization for states arbitrarily far from equilibrium, LRT extends the successful concepts of statistical mechanics to situations close to equilibrium. In our work, we connect these cornerstones to shed light on the route to equilibrium for a class…

## 15 Citations

Eigenstate thermalization and quantum chaos in the Holstein polaron model

- PhysicsPhysical Review B
- 2019

The eigenstate thermalization hypothesis (ETH) is a successful theory that provides sufficient criteria for ergodicity in quantum many-body systems. Most studies were carried out for Hamiltonians…

Quantitative Impact of Integrals of Motion on the Eigenstate Thermalization Hypothesis.

- PhysicsPhysical review letters
- 2020

A generic protocol is introduced to construct observables, subtracted by their projections on LIoms as well as products of LIOMs, and systematically reduces fluctuations and/or the structure of the diagonal matrix elements of local observables.

Relaxation of dynamically prepared out-of-equilibrium initial states within and beyond linear response theory.

- PhysicsPhysical review. E
- 2019

A realistic nonequilibrium protocol, where a quantum system in thermal equilibrium is suddenly subjected to an external force, shows that expectation values thermalize to their original equilibrium values, despite the eigenstate thermalization hypothesis being violated.

Eigenstate thermalization hypothesis and integrals of motion

- Physics
- 2019

Even though foundations of the eigenstate thermalization hypothesis (ETH) are based on random matrix theory, physical Hamiltonians and observables substantially differ from random operators. One of…

Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions.

- Physics, MathematicsPhysical review. E
- 2021

This work studies the distribution of matrix elements for a class of operators in dual-unitary quantum circuits in dependence of the frequency associated with the corresponding eigenstates, and provides an exact asymptotic expression for the spectral function.

Exponential damping induced by random and realistic perturbations.

- PhysicsPhysical review. E
- 2020

This work studies the decay of current autocorrelation functions in spin-1/2 ladder systems and finds a convincing agreement between the exact dynamics and the lowest-order prediction over a wide range of interchain couplings.

Time Evolution of Correlation Functions in Quantum Many-Body Systems.

- Mathematics, PhysicsPhysical review letters
- 2020

It is shown that in a large class of translation-invariant models the correlation functions factorize at late times, thus proving that dissipation emerges out of the unitary dynamics of the system, and an upper bound on the timescale at which they reach the factorized late time value is provided.

Eigenstate thermalization hypothesis beyond standard indicators: Emergence of random-matrix behavior at small frequencies.

- PhysicsPhysical review. E
- 2020

It is demonstrated that at much smaller energy scales, the eigenvalue distribution approximately assumes the universal semicircle shape, indicating transition to the random-matrix behavior, and in particular that matrix elements become uncorrelated.

Decoherence entails exponential forgetting in systems complying with the eigenstate thermalization hypothesis

- PhysicsPhysical Review A
- 2019

According to the eigenstate thermalization ansatz, matrices representing generic few body observables take on a specific form when displayed in the eigenbasis of a chaotic Hamiltonian. We examine the…

Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters

- Physics
- 2020

We study quantum quenches in the transverse-field Ising model defined on different lattice geometries such as chains, two- and three-leg ladders, and two-dimensional square lattices. Starting from…

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