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arXiv · 2112.07646

Fast Thermalization from the Eigenstate Thermalization Hypothesis

Chi-Fang Chen·Fernando G. S. L. Brandão
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Abstract

The Eigenstate Thermalization Hypothesis (ETH) has played a major role in understanding thermodynamic phenomena in closed quantum systems. However, its connection to the timescale of thermalization for open system dynamics has remained elusive. This paper establishes a rigorous link between ETH and fast thermalization to the global Gibbs state. Specifically, we demonstrate fast thermalization for a system coupled weakly to a bath of quasi-free Fermions that we refresh periodically. To describe the joint evolution, we derive a finite-time version of Davies' generator with explicit error bounds and resource estimates. Our approach exploits a critical feature of ETH: operators in the energy basis can be modeled by independent random matrices in a near-diagonal band. This gives quantum expanders at nearby eigenstates of the Hamiltonian and reduces the problem to a one-dimensional classical random walk on the energy eigenstates. Our results explain finite-time thermalization in chaotic open quantum systems.

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BibTeXRIS

Chi-Fang Chen, Fernando G. S. L. Brandão. 2021-12-14. Fast Thermalization from the Eigenstate Thermalization Hypothesis. https://arxiv.org/abs/2112.07646

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