Time Fluctuations in Isolated Quantum Systems of Interacting Particles

TL;DR

This paper investigates how time fluctuations of observables decay exponentially with system size in isolated quantum systems, revealing differences between integrable and chaotic regimes and linking decay rates to initial state delocalization.

Contribution

It demonstrates exponential decay of time fluctuations in both integrable and chaotic systems and relates decay coefficients to initial state properties.

Findings

Fluctuations decay exponentially with system size in both regimes.

Integrable systems with Bethe ansatz have nondegenerate spectra.

Decay coefficient depends on initial state delocalization.

Abstract

Numerically, we study the time fluctuations of few-body observables after relaxation in isolated dynamical quantum systems of interacting particles. Our results suggest that they decay exponentially with system size in both regimes, integrable and chaotic. The integrable systems considered are solvable with the Bethe ansatz and have a highly nondegenerate spectrum. This is in contrast with integrable Hamiltonians mappable to noninteracting ones. We show that the coefficient of the exponential decay depends on the level of delocalization of the initial state with respect to the energy shell.