Non-Hermitian Hamiltonians violate the eigenstate thermalization hypothesis

Abstract

The eigenstate thermalization hypothesis (ETH) represents a cornerstone in the theoretical understanding of the emergence of thermal behavior in closed quantum systems. Here, the authors investigate to what extent the ETH holds for non-Hermitian Hamiltonians, relevant for open and monitored quantum systems, and come to the surprising conclusion that fluctuations are greatly enhanced, indicating the breakdown of thermalization.