Explicit solution of the time evolution of the Wigner function
Abstract
Previously, an explicit solution for the time evolution of the Wigner function was presented in terms of auxiliary phase space coordinates which obey simple equations that are analogous with, but not identical to, the classical equations of motion. They can be solved easily, and their solutions can be used to construct the time evolution of the Wigner function. In this paper, the usefulness of this explicit solution is demonstrated by solving a numerical example in which the Wigner function has strong spatial and temporal variations as well as regions with negative values. It is found that the explicit solution gives a correct description of the time evolution of the Wigner function. We examine next the pseudoparticle method which uses classical trajectories to evolve the Wigner function. We find that the lowest-order pseudoparticle approximation reproduces the general features of the time evolution, but there are deviations. We show how these deviations can be systematically reduced by including higher-order correction terms in powers of hbar2.
- Publication:
-
Journal of Optics B: Quantum and Semiclassical Optics
- Pub Date:
- June 2003
- DOI:
- 10.1088/1464-4266/5/3/381
- arXiv:
- arXiv:quant-ph/0210112
- Bibcode:
- 2003JOptB...5S.420W
- Keywords:
-
- Wigner function;
- time evolution;
- methods in quantum theory;
- Quantum Physics;
- Condensed Matter;
- High Energy Physics - Phenomenology;
- Mathematical Physics;
- Nuclear Theory
- E-Print:
- 16 pages, in LaTex, invited talk presented at the Wigner Centennial Conference, Pecs, Hungary, July 8-12, 2002, to be published in the Journal of Optics B: Quantum and Classical Optics, June 2003