Eigenstate Thermalisation on Average
Joe Dunlop, Oliver Cohen, Anthony J. Short
TL;DR
This paper explores conditions for quantum systems to reach thermal equilibrium, focusing on a weaker eigenstate thermalisation hypothesis based on average properties, and examines its role in thermalisation.
Contribution
It introduces a weaker, average-based eigenstate thermalisation hypothesis and analyzes its necessity and sufficiency for quantum thermalisation.
Findings
The average eigenstate thermalisation hypothesis is sufficient for thermalisation.
The weaker hypothesis is necessary under certain conditions.
The paper clarifies the relationship between eigenstate properties and thermal equilibrium.
Abstract
We consider conditions under which an isolated quantum system approaches a microcanonical equilibrium state. A key component is the eigenstate thermalisation hypothesis, which proposes that all energy eigenstates appear thermal. We introduce a weaker version of this requirement, applying only to the average distinguishability of eigenstates from the thermal state, and investigate its necessity and sufficiency for thermalisation.
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