Mathew R, Tiesinga E
Joint Quantum Institute, University of Maryland and National Institute of Standards and Technology, College Park, MD 20742, United States of America.
Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, National Institute of Standards and Technology and University of Maryland, Gaithersburg, MD 20899, United States of America.
J Phys B At Mol Opt Phys. 2019;52(18). doi: https://doi.org/10.1088/1361-6455/ab319c.
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.
我们研究了在半经典区域中玻色子动力学的相空间表示，其中模式的占据数很大。为此，我们采用范弗莱克 - 古兹维勒传播子来获得维格纳分布的格林函数的近似值。半经典分析考虑了经典路径的干涉，当忽略干涉时可简化为截断维格纳近似（TWA）。此外，我们确定了TWA失效后的埃伦费斯特时间。作为一个案例研究，我们考虑一个单模量子非线性振荡器，它表现出可观测量的坍缩和复苏。我们通过分析表明，经典路径的干涉导致了复苏，这一效应无法通过TWA或微扰分析再现。
