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

A semiclassical theory of phase-space dynamics of interacting bosons