How Wigner Functions Transform Under Symplectic Maps

Details How Wigner Functions Transform Under Symplectic Maps How Wigner Functions Transform Under Symplectic Maps

1998-06-16

arxiv.org/abs/quant-ph/9806056v1

Physics

Quantum Physics

8 pages, 6 figures [RevTeX/epsfig, macro included]. To appear in Proceedings of the Advanced Beam Dynamics Workshop on Quantum

Scientific paper

It is shown that, while Wigner and Liouville functions transform in an identical way under linear symplectic maps, in general they do not transform identically for nonlinear symplectic maps. Instead there are ``quantum corrections'' whose hbar tending to zero limit may be very complicated. Examples of the behavior of Wigner functions in this limit are given in order to examine to what extent the corresponding Liouville densities are recovered.

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