Semiclassical propagator of the Wigner function

Details Semiclassical propagator of the Wigner function Semiclassical propagator of the Wigner function

2005-08-06

arxiv.org/abs/quant-ph/0508057v2

Phys. Rev. Lett. 96, 070403 (2006)

Physics

Quantum Physics

4 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.96.070403

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.

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