dorsal/arxiv
View SchemaExplicit Solution of the Time Evolution of the Wigner Function
| Authors | Cheuk-Yin Wong |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0210112 |
| URL | https://arxiv.org/abs/quant-ph/0210112 |
| DOI | 10.1088/1464-4266/5/3/381 |
| Journal | J.Optics B5 (2003) S420 |
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 utilized 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 approximation which uses classical trajectories to evolve the Wigner function. We find that the 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 $\hbar^2$.
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"abstract": "Previously, an explicit solution for the time evolution of the Wigner\nfunction was presented in terms of auxiliary phase space coordinates which obey\nsimple equations that are analogous with, but not identical to, the classical\nequations of motion. They can be solved easily and their solutions can be\nutilized to construct the time evolution of the Wigner function. In this paper,\nthe usefulness of this explicit solution is demonstrated by solving a numerical\nexample in which the Wigner function has strong spatial and temporal variations\nas well as regions with negative values. It is found that the explicit solution\ngives a correct description of the time evolution of the Wigner function. We\nexamine next the pseudoparticle approximation which uses classical trajectories\nto evolve the Wigner function. We find that the pseudoparticle approximation\nreproduces the general features of the time evolution, but there are\ndeviations. We show how these deviations can be systematically reduced by\nincluding higher-order correction terms in powers of $\\hbar^2$.",
"arxiv_id": "quant-ph/0210112",
"authors": [
"Cheuk-Yin Wong"
],
"categories": [
"quant-ph",
"cond-mat",
"hep-ph",
"math-ph",
"math.MP",
"nucl-th"
],
"doi": "10.1088/1464-4266/5/3/381",
"journal_ref": "J.Optics B5 (2003) S420",
"title": "Explicit Solution of the Time Evolution of the Wigner Function",
"url": "https://arxiv.org/abs/quant-ph/0210112"
},
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