Phase-space path-integral calculation of the Wigner function

DOI10.1088/0305-4470/36/42/015zbMATH Open1047.81529arXivquant-ph/0308119OpenAlexW2155775584MaRDI QIDQ4468657

Publication date: 10 June 2004

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/quant-ph/0308119

Mathematics Subject Classification ID

Path integrals in quantum mechanics (81S40) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30)