Quantum unitary evolution interspersed with repeated non-unitary interactions at random times

Abstract

What happens when the unitary evolution of a generic closed quantum system is interrupted at random times with non-unitary evolution due to interactions with either the external environment or a measuring apparatus? We adduce a general framework to obtain the average density operator of a generic quantum system experiencing any form of non-unitary interaction. We provide two explicit applications in the context of the tight-binding model for two representative forms of interactions: (i) stochastic resets and (ii) projective measurements at random times. For the resetting case, our exact results show how the particle is localized on the sites at long times, leading to a time-independent mean-squared displacement. For the projective measurement case, repeated projection to the initial state results in an effective suppression of the temporal decay in the probability of the particle being in the initial state. The amount of suppression is comparable to the one in conventional Zeno effect scenarios, where measurements are performed at regular intervals.