Bound on Eigenstate Thermalization from Transport

Anatoly Dymarsky

Published 2018-04-23Version 1

We show that presence of transport imposes constraints on matrix elements entering the Eigenstate Thermalization Hypothesis (ETH) ansatz and require them to be correlated. It is generally assumed that the ETH ansatz reduces to Random Matrix Theory (RMT) below the Thouless energy scale. We show this conventional picture is not self-consistent. We prove that the energy scale at which ETH ansatz reduces to RMT has to be parametrically smaller than the inverse timescale of the slowest thermalization mode present in the system. In particular it has to be parametrically smaller than the Thouless energy. Our results indicate there is a new scale relevant for thermalization dynamics.