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

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.