Semiclassical propagator of the Wigner function

Dittrich, Thomas; Sandoval, Luis; Viviescas, Carlos

Semiclassical propagator of the Wigner function

Authors

Dittrich, Thomas

Sandoval, Luis

Viviescas, Carlos

Description

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