dorsal/arxiv
View SchemaQuantum State Diffusion, Density Matrix Diagonalization and Decoherent Histories: A Model
| Authors | Jonathan Halliwell, Andreas Zoupas |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9503008 |
| URL | https://arxiv.org/abs/quant-ph/9503008 |
| DOI | 10.1103/PhysRevD.52.7294 |
| Journal | Phys.Rev.D52:7294-7307,1995 |
Abstract
We analyse the quantum evolution of a particle moving in a potential in interaction with an environment of harmonic oscillators in a thermal state, using the quantum state diffusion (QSD) picture of Gisin and Percival, in which one associates the usual Markovian master equation for the density operator with a class of stochastic non-linear Schr\"odinger equations. We find stationary solutions to the Ito equation which are Gaussians, localized around a point in phase space undergoing classical Brownian motion. We show that every initial state approaches these stationary solutions in the long time limit. We recover the density operator corresponding to these solutions, and thus show, for this particular model, that the QSD picture effectively supplies a prescription for approximately diagonalizing the density operator in a basis of phase space localized states. The rate of localization is related to the decoherence time, and also to the timescale on which thermal and quantum fluctuations become comparable. We use these results to exemplify the general connection between the QSD picture and the decoherent histories approach.
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"abstract": "We analyse the quantum evolution of a particle moving in a potential in\ninteraction with an environment of harmonic oscillators in a thermal state,\nusing the quantum state diffusion (QSD) picture of Gisin and Percival, in which\none associates the usual Markovian master equation for the density operator\nwith a class of stochastic non-linear Schr\\\"odinger equations. We find\nstationary solutions to the Ito equation which are Gaussians, localized around\na point in phase space undergoing classical Brownian motion. We show that every\ninitial state approaches these stationary solutions in the long time limit. We\nrecover the density operator corresponding to these solutions, and thus show,\nfor this particular model, that the QSD picture effectively supplies a\nprescription for approximately diagonalizing the density operator in a basis of\nphase space localized states. The rate of localization is related to the\ndecoherence time, and also to the timescale on which thermal and quantum\nfluctuations become comparable. We use these results to exemplify the general\nconnection between the QSD picture and the decoherent histories approach.",
"arxiv_id": "quant-ph/9503008",
"authors": [
"Jonathan Halliwell",
"Andreas Zoupas"
],
"categories": [
"quant-ph",
"gr-qc"
],
"doi": "10.1103/PhysRevD.52.7294",
"journal_ref": "Phys.Rev.D52:7294-7307,1995",
"title": "Quantum State Diffusion, Density Matrix Diagonalization and Decoherent Histories: A Model",
"url": "https://arxiv.org/abs/quant-ph/9503008"
},
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