dorsal/arxiv
View SchemaExact solution of the Hu-Paz-Zhang master equation
| Authors | G. W. Ford, R. F. O'Connell |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0301053 |
| URL | https://arxiv.org/abs/quant-ph/0301053 |
| DOI | 10.1103/PhysRevD.64.105020 |
| Journal | Phys.Rev.D 64,105020 (2001) |
Abstract
The Hu-Paz-Zhang equation is a master equation for an oscillator coupled to a linear passive bath. It is exact within the assumption that the oscillator and bath are initially uncoupled . Here an exact general solution is obtained in the form of an expression for the Wigner function at time t in terms of the initial Wigner function. The result is applied to the motion of a Gaussian wave packet and to that of a pair of such wave packets. A serious divergence arising from the assumption of an initially uncoupled state is found to be due to the zero-point oscillations of the bath and not removed in a cutoff model. As a consequence, worthwhile results for the equation can only be obtained in the high temperature limit, where zero-point oscillations are neglected. In that limit closed form expressions for wave packet spreading and attenuation of coherence are obtained. These results agree within a numerical factor with those appearing in the literature, which apply for the case of a particle at zero temperature that is suddenly coupled to a bath at high temperature. On the other hand very different results are obtained for the physically consistent case in which the initial particle temperature is arranged to coincide with that of the bath.
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"abstract": "The Hu-Paz-Zhang equation is a master equation for an oscillator coupled to a\nlinear passive bath. It is exact within the assumption that the oscillator and\nbath are initially uncoupled . Here an exact general solution is obtained in\nthe form of an expression for the Wigner function at time t in terms of the\ninitial Wigner function. The result is applied to the motion of a Gaussian wave\npacket and to that of a pair of such wave packets. A serious divergence arising\nfrom the assumption of an initially uncoupled state is found to be due to the\nzero-point oscillations of the bath and not removed in a cutoff model. As a\nconsequence, worthwhile results for the equation can only be obtained in the\nhigh temperature limit, where zero-point oscillations are neglected. In that\nlimit closed form expressions for wave packet spreading and attenuation of\ncoherence are obtained. These results agree within a numerical factor with\nthose appearing in the literature, which apply for the case of a particle at\nzero temperature that is suddenly coupled to a bath at high temperature. On the\nother hand very different results are obtained for the physically consistent\ncase in which the initial particle temperature is arranged to coincide with\nthat of the bath.",
"arxiv_id": "quant-ph/0301053",
"authors": [
"G. W. Ford",
"R. F. O\u0027Connell"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevD.64.105020",
"journal_ref": "Phys.Rev.D 64,105020 (2001)",
"title": "Exact solution of the Hu-Paz-Zhang master equation",
"url": "https://arxiv.org/abs/quant-ph/0301053"
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