Bound on Eigenstate Thermalization from Transport
arXiv:1804.08626 · doi:10.1103/PhysRevLett.128.190601
Abstract
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 this conventional picture is not self-consistent. We prove that 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 hydrodynamic description of transport breaks down.
v2 journal version, presentation improved, interpretation of T_{RMT} added
References in corpus (15)
- Thermalization and its mechanism for generic isolated quantum systems
- Chaos, Complexity, and Random Matrices
- Anomalous thermalization in ergodic systems
- Off-diagonal matrix elements of local operators in many-body quantum systems
- The Eigenstate Thermalization Hypothesis and Out of Time Order Correlators
- Thouless and relaxation time scales in many-body quantum systems
- Eigenstate thermalization hypothesis beyond standard indicators: Emergence of random-matrix behavior at small frequencies
- Eigenstate Correlations, Thermalization and the Butterfly Effect
- Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time
- Heavy Operators and Hydrodynamic Tails
- Out-of-time-order correlations and the fine structure of eigenstate thermalisation
- Operator Spreading in Quantum Maps
- Eigenstate thermalization and rotational invariance in ergodic quantum systems
- Equilibration time in many-body quantum systems
- Nonequilibrium many-body quantum dynamics: from full random matrices to real systems
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