Semiclassical propagator of the Wigner function

Abstract

Propagation of the Wigner function is studied on two levels of semiclassical propagation, one based on the van-Vleck propagator, the other on phase-space path integration. Leading quantum corrections to the classical Liouville propagator take the form of a time-dependent quantum spot. Its oscillatory structure depends on whether the underlying classical flow is elliptic or hyperbolic. It can be interpreted as the result of interference of a \emph{pair} of classical trajectories, indicating how quantum coherences are to be propagated semiclassically in phase space. The phase-space path-integral approach allows for a finer resolution of the quantum spot in terms of Airy functions.

4 pages, 3 figures

References in corpus (5)

• Sub-Planck spots of Schroedinger cats and quantum decoherence
• Semiclassical Approximations in Phase Space with Coherent States
• On the propagation of semiclassical Wigner functions
• Solving quantum master equations in phase space by continued-fraction methods
• Wigner function for discrete phase space: exorcising ghost images

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