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

preprint

posted on 2006-06-29, 10:36 authored by John SamsonThe 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.

## History

## School

- Science

## Department

- Physics

## Pages

245099 bytes## Publication date

2003## Notes

This is a pre-print. The definitive version: SAMSON (2003), Phase-space path-integral 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.## Language

- en