Eigenstate Thermalization Hypothesis and Free Probability

Pappalardi, Silvia; Foini, Laura; Kurchan, Jorge

doi:10.1103/physrevlett.129.170603

Cited by 34 publications

(17 citation statements)

References 46 publications

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“…In a certain limit, the three-point functions above should reduce to derivatives of two-point functions with respect to chemical potential (18). From (A.11), one finds that this is indeed the case i lim…”

Section: Generalizationsmentioning

confidence: 85%

“…Generalized fluctuation-dissipation or KMS relations were found in [15,16]. Certain general properties were also studied recently through the lens of the eigenstate thermalization hypothesis in [17,18]. Higher order correlation functions were computed in holographic models [19,20], models with relaxational dynamics [19,21], integrable systems [22,23] as well as more general ballistic regimes [24].…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear response in diffusive systems

Delacrétaz,

Mishra

2024

SciPost Phys.

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Nonintegrable systems thermalize, leading to the emergence of fluctuating hydrodynamics. Typically, this hydrodynamics is diffusive. We use the effective field theory (EFT) of diffusion to compute higher-point functions of conserved densities. We uncover a simple scaling behavior of correlators at late times, and, focusing on three and four-point functions, derive the asymptotically exact universal scaling functions that characterize nonlinear response in diffusive systems. This allows for precision tests of thermalization beyond linear response in quantum and classical many-body systems. We confirm our predictions in a classical lattice gas.

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Section: Generalizationsmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Nonlinear response in diffusive systems

Delacrétaz,

Mishra

2024

SciPost Phys.

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“…It also has potential applications in many-body systems at equilibrium satisfying the ETH. Indeed, as recently understood [27,28], a proper formulation of this hypothesis involves notions from free probability. We showed in appendix A how to evaluate, within ETH, canonical or micro-canonical expectation values of observables in terms of their local free cumulants.…”

Section: Discussionmentioning

confidence: 99%

“…However, it has recently been understood [27,28] that the original formulation of ETH needs to be generalized in order to be able to deal with multi-time correlation functions of say collections of operators A α at different times t α : namely, tr(ρ…”

Section: A Application To the Eigenstate Thermalization Hypothesis (Eth)mentioning

confidence: 99%

Exact entanglement in the driven quantum symmetric simple exclusion process

Bernard,

Hruza

2023

SciPost Phys.

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Entanglement properties of driven quantum systems can potentially differ from the equilibrium situation due to long range coherences. We confirm this observation by studying a suitable toy model for mesoscopic transport: the open quantum symmetric simple exclusion process (QSSEP). We derive exact formulae for its mutual information between different subsystems in the steady state and show that it satisfies a volume law. Surprisingly, the QSSEP entanglement properties only depend on data related to its transport properties and we suspect that such a relation might hold for more general mesoscopic systems. Exploiting the free probability structure of QSSEP, we obtain these results by developing a new method to determine the eigenvalue spectrum of sub-blocks of random matrices from their so-called local free cumulants – a mathematical result on its own with potential applications in the theory of random matrices. As an illustration of this method, we show how to compute expectation values of observables in systems satisfying the Eigenstate Thermalization Hypothesis (ETH) from the local free cumulants.

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“…Recently, the ETH has also been generalized for non-commuting conserved charges [231]. Moreover, ongoing studies have unveiled structure beyond ETH, encompassing the statistical correlations between the matrix elements of the observables as well as the energy eigenstates [232][233][234][235].…”

Section: Ergodicity and Thermalizationmentioning

confidence: 99%

Classical route to ergodicity and scarring in collective quantum systems

Sinha,

Ray,

Sinha

2024

J. Phys.: Condens. Matter

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Ergodicity, a fundamental concept in statistical mechanics, is not yet a fully understood phenomena for closed quantum systems, particularly its connection with the underlying chaos. In this review, we consider a few examples of collective quantum systems to unveil the intricate relationship of ergodicity as well as its deviation due to quantum scarring phenomena with their classical counterpart. A comprehensive overview of classical and quantum chaos is provided, along with the tools essential for their detection. Furthermore, we survey recent theoretical and experimental advancements in the domain of ergodicity and its violations. This review aims to illuminate the classical perspective of quantum scarring phenomena in interacting quantum systems.

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Eigenstate Thermalization Hypothesis and Free Probability

Cited by 34 publications

References 46 publications

Nonlinear response in diffusive systems

Nonlinear response in diffusive systems

Exact entanglement in the driven quantum symmetric simple exclusion process

Classical route to ergodicity and scarring in collective quantum systems

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