Phase-space path-integral calculation of the Wigner function

Details Phase-space path-integral calculation of the Wigner function Phase-space path-integral calculation of the Wigner function

2003-08-22

arxiv.org/abs/quant-ph/0308119v2

Journal of Physics A: Mathematical and General, 36, 10637 - 10650 (2003)

Physics

Quantum Physics

16 pages. Small number of typos corrected, including sign in eq A21

Scientific paper

10.1088/0305-4470/36/42/015

The Wigner function W(q,p) is formulated as a phase-space 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 path-centroid method in the configuration-space path integral. Paths can be classified by the mid-point of their ends; short paths where the mid-point 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.

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