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

Takaaki Monnai

Published 2018-02-28Version 1

The eigenstate thermalization hypothesis (ETH) suggests that each energy eigenstate is a superposition of sufficient number of macroscopically similar and mutually orthogonal pure states. For isolated quantum many-body systems, we show that the energy eigenstates are superposition of uncountably many quasi eigenstates of operationally defined "time operator", which are thermal and approximately orthogonal in terms of extremely short relaxation time of the fidelity. In this way, our scenario gives a foundation of ETH.