On the propagation of semiclassical Wigner functions

Details On the propagation of semiclassical Wigner functions On the propagation of semiclassical Wigner functions

2001-11-07

arxiv.org/abs/math-ph/0111012v2

J.Phys A: Math. Gen. 35 (2002) 2609-2617

Physics

Mathematical Physics

9 pages, 1 figure. To appear in J. Phys. A. This version matches the one set to print and differs from the previous one (07 No

Scientific paper

10.1088/0305-4470/35/11/307

We establish the difference between the propagation of semiclassical Wigner functions and classical Liouville propagation. First we re-discuss the semiclassical limit for the propagator of Wigner functions, which on its own leads to their classical propagation. Then, via stationary phase evaluation of the full integral evolution equation, using the semiclassical expressions of Wigner functions, we provide the correct geometrical prescription for their semiclassical propagation. This is determined by the classical trajectories of the tips of the chords defined by the initial semiclassical Wigner function and centered on their arguments, in contrast to the Liouville propagation which is determined by the classical trajectories of the arguments themselves.

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