dorsal/arxiv
View SchemaThe Post-Decoherence Density Matrix Propagator for Quantum Brownian Motion
| Authors | Jonathan Halliwell, Andreas Zoupas |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9608046 |
| URL | https://arxiv.org/abs/quant-ph/9608046 |
| DOI | 10.1103/PhysRevD.55.4697 |
| Journal | Phys.Rev.D55:4697-4704,1997 |
Abstract
Using the path integral representation of the density matrix propagator of quantum Brownian motion, we derive its asymptotic form for times greater than the localization time, $ (\hbar / \gamma k T )^{\half}$, where $\gamma$ is the dissipation and $T$ the temperature of the thermal environment. The localization time is typically greater than the decoherence time, but much shorter than the relaxation time, $\gamma^{-1}$. We use this result to show that the reduced density operator rapidly evolves into a state which is approximately diagonal in a set of generalized coherent states. We thus reproduce, using a completely different method, a result we previously obtained using the quantum state diffusion picture (Phys.Rev. D52, 7294 (1995)). We also go beyond this earlier result, in that we derive an explicit expression for the weighting of each phase space localized state in the approximately diagonal density matrix, as a function of the initial state. For sufficiently long times it is equal to the Wigner function, and we confirm that the Wigner function is positive for times greater than the localization time (multiplied by a number of order 1).
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"abstract": "Using the path integral representation of the density matrix propagator of\nquantum Brownian motion, we derive its asymptotic form for times greater than\nthe localization time, $ (\\hbar / \\gamma k T )^{\\half}$, where $\\gamma$ is the\ndissipation and $T$ the temperature of the thermal environment. The\nlocalization time is typically greater than the decoherence time, but much\nshorter than the relaxation time, $\\gamma^{-1}$. We use this result to show\nthat the reduced density operator rapidly evolves into a state which is\napproximately diagonal in a set of generalized coherent states. We thus\nreproduce, using a completely different method, a result we previously obtained\nusing the quantum state diffusion picture (Phys.Rev. D52, 7294 (1995)). We also\ngo beyond this earlier result, in that we derive an explicit expression for the\nweighting of each phase space localized state in the approximately diagonal\ndensity matrix, as a function of the initial state. For sufficiently long times\nit is equal to the Wigner function, and we confirm that the Wigner function is\npositive for times greater than the localization time (multiplied by a number\nof order 1).",
"arxiv_id": "quant-ph/9608046",
"authors": [
"Jonathan Halliwell",
"Andreas Zoupas"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevD.55.4697",
"journal_ref": "Phys.Rev.D55:4697-4704,1997",
"title": "The Post-Decoherence Density Matrix Propagator for Quantum Brownian Motion",
"url": "https://arxiv.org/abs/quant-ph/9608046"
},
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