Eigenstate thermalization hypothesis, time operator, and extremely quick relaxation of fidelity

TL;DR

This paper proposes a theoretical explanation for the eigenstate thermalization hypothesis (ETH) by linking energy eigenstates to superpositions of quasi eigenstates of a time operator, explaining rapid thermalization in quantum many-body systems.

Contribution

It introduces a novel scenario connecting the ETH to superpositions of time operator eigenstates, providing a new understanding of thermalization mechanisms.

Findings

Energy eigenstates are superpositions of quasi eigenstates of a time operator.

Quasi eigenstates are thermal for isolated quantum systems.

Fidelity relaxes extremely quickly, supporting the superposition hypothesis.

Abstract

The eigenstate thermalization hypothesis (ETH) insists that for nonintegrable systems each energy eigenstate accurately gives microcanonical expectation values for a class of observables. As a mechanism for ETH to hold, we show that the energy eigenstates are superposition of uncountably many quasi eigenstates of operationally defined "time operator", which are thermal for thermodynamic isolated quantum many-body systems and approximately orthogonal in terms of extremely short relaxation time of the fidelity. In this way, our scenario provides a theoretical explanation of ETH.