Quantum dynamics with stochastic reset

TL;DR

This paper investigates how stochastic resets affect the long-term behavior of quantum systems, showing that non-integrable systems do not thermalize and integrable systems reach generalized Gibbs states, with implications for experiments.

Contribution

It introduces a framework for understanding quantum dynamics under stochastic resets, revealing non-thermalization in non-integrable systems and generalized Gibbs states in integrable models.

Findings

Non-integrable systems retain off-diagonal elements in steady state density matrix at finite reset rate.

Observable expectation values do not thermalize under reset dynamics.

Density profiles in fermionic chains approach a nonequilibrium stationary state.

Abstract

We study non-equilibrium dynamics of integrable and non-integrable closed quantum systems whose unitary evolution is interrupted with stochastic resets, characterized by a reset rate $r$, that project the system to its initial state. We show that the steady state density matrix of a non-integrable system, averaged over the reset distribution, retains its off-diagonal elements for any finite $r$. Consequently a generic observable $\hat O$, whose expectation value receives contribution from these off-diagonal elements, never thermalizes under such dynamics for any finite $r$. We demonstrate this phenomenon by exact numerical studies of experimentally realizable models of ultracold bosonic atoms in a tilted optical lattice. For integrable Dirac-like fermionic models driven periodically between such resets, the reset-averaged steady state is found to be described by a family of generalized Gibbs ensembles (GGE s) characterized by $r$. We also study the spread of particle density of a non-interacting one-dimensional fermionic chain, starting from an initial state where all fermions occupy the left half of the sample, while the right half is empty. When driven by resetting dynamics, the density profile approaches at long times to a nonequilibrium stationary profile that we compute exactly. We suggest concrete experiments that can possibly test our theory.