Quantum phase-space analysis of population equilibration in multi-well ultracold atomic systems

TL;DR

This paper investigates the quantum dynamics and population equilibration in multi-well Bose-Hubbard models, revealing how initial conditions influence the approach to equilibrium and introducing an effective entropy measure.

Contribution

It introduces a stochastic phase-space method to analyze population dynamics and constructs an effective entropy to quantify equilibration in multi-well ultracold atomic systems.

Findings

All systems reach at least a temporary equilibrium.

Classical integrability does not predict equilibration.

Effective entropy quantifies the approach to equilibrium.

Abstract

We examine the medium time quantum dynamics and population equilibration of two, three and four-well Bose-Hubbard models using stochastic integration in the truncated Wigner phase-space representation. We find that all three systems will enter at least a temporary state of equilibrium, with the details depending on both the classical initial conditions and the initial quantum statistics. We find that classical integrability is not necessarily a good guide as to whether equilibration will occur. We construct an effective single-particle reduced density matrix for each of the systems, using the expectation values of operator moments, and use this to calculate an effective entropy. Knowing the expected maximum values of this entropy for each system, we are able to quantify the different approaches to equilibrium.