Bound on Eigenstate Thermalization from Transport

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11 Scopus citations


We show that macroscopic thermalization and transport impose constraints on matrix elements entering the eigenstate thermalization hypothesis (ETH) ansatz and require them to be correlated. It is often assumed that the ETH reduces to random matrix theory (RMT) below the Thouless energy scale. We show that this conventional picture is not self-consistent. We prove that the energy scale at which the RMT behavior emerges has to be parametrically smaller than the inverse timescale of the slowest thermalization mode coupled to the operator of interest. We argue that the timescale marking the onset of the RMT behavior is the same timescale at which the hydrodynamic description of transport breaks down.

Original languageEnglish
Article number190601
JournalPhysical Review Letters
Issue number19
StatePublished - May 13 2022

Bibliographical note

Funding Information:
I thank Y. Bar Lev, A. Polkovnikov, and A. Shapere for reading the manuscript. I also thank the University of Kentucky Center for Computational Sciences for computing time on the Lipscomb High Performance Computing Cluster. I gratefully acknowledge support and hospitality of the Simons Center for Geometry and Physics, Stony Brook University at which part of the research for this Letter was performed. This research is supported by the National Science Foundation under Grant No. PHY-2013812.

Publisher Copyright:
© 2022 American Physical Society.

ASJC Scopus subject areas

  • Physics and Astronomy (all)


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