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Title:  Phasespace pathintegral calculation of the Wigner function 
Authors:  Samson, J.H. 
Issue Date:  2003 
Abstract:  The Wigner function W(q,p) is formulated as a phasespace path integral, whereby its sign oscillations can be seen to follow from interference between the geometrical phases of the paths. The approach has similarities to the pathcentroid method in the configurationspace path integral. Paths can be classified by the midpoint of their ends; short paths where the midpoint is close to (q,p) and which lie in regions of low energy (low P function of the Hamiltonian) will dominate, and the enclosed area will determine the sign of the Wigner function. As a demonstration, the method is applied to a sequence of density matrices interpolating between a Poissonian number distribution and a number state, each member of which can be represented exactly by a discretized path integral with a finite number of vertices. Saddle point evaluation of these integrals recovers (up to a constant factor) the WKB approximation to the Wigner function of a number state. 
Description:  This is a preprint. The definitive version: SAMSON (2003), Phasespace pathintegral calculation of the Wigner function. Journal of Physics A: Mathematical and General, 36, 10637  10650, is available at: http://www.iop.org/EJ/journal/JPhysA. 
URI:  https://dspace.lboro.ac.uk/2134/2229 
Appears in Collections:  PrePrints (Physics)

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