A semiclassical theory of phase-space dynamics of interacting bosons

TL;DR

This paper develops a semiclassical phase-space framework for interacting bosons, capturing interference effects and identifying the limits of the truncated Wigner approximation, with applications to quantum revivals in nonlinear oscillators.

Contribution

It introduces a semiclassical approach using the van Vleck-Gutzwiller propagator to analyze bosonic dynamics, including interference effects and the Ehrenfest time.

Findings

Interference of classical paths causes quantum revivals.

The truncated Wigner approximation fails after the Ehrenfest time.

Analytical demonstration of revivals in a nonlinear oscillator.

Abstract

We study the phase-space representation of dynamics of bosons in the semiclassical regime where the occupation number of the modes is large. To this end, we employ the van Vleck-Gutzwiller propagator to obtain an approximation for the Green's function of the Wigner distribution. The semiclassical analysis incorporates interference of classical paths and reduces to the truncated Wigner approximation (TWA) when the interference is ignored. Furthermore, we identify the Ehrenfest time after which the TWA fails. As a case study, we consider a single-mode quantum nonlinear oscillator, which displays collapse and revival of observables. We analytically show that the interference of classical paths leads to revivals, an effect that is not reproduced by the TWA or a perturbative analysis.