dorsal/arxiv
View SchemaTwo Derivations of the Master Equation of Quantum Brownian Motion
| Authors | J. J. Halliwell |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0607132 |
| URL | https://arxiv.org/abs/quant-ph/0607132 |
| DOI | 10.1088/1751-8113/40/12/S11 |
Abstract
Central to many discussion of decoherence is a master equation for the reduced density matrix of a massive particle experiencing scattering from its surrounding environment, such as that of Joos and Zeh. Such master equations enjoy a close relationship with spontaneous localization models, like the GRW model. This aim of this paper is to present two derivations of the master equation. The first derivation is a pedagogical model designed to illustrate the origins of the master equation as simply as possible, focusing on physical principles and without the complications of S-matrix theory. This derivation may serve as a useful tutorial example for students attempting to learn this subject area. The second is the opposite: a very general derivation using non-relativistic many body field theory. It reduces to the equation of the type given by Joos and Zeh in the one-particle sector, but correcting certain numerical factors which have recently become significant in connection with experimental tests of decoherence. This master equation also emphasizes the role of local number density as the ``preferred basis'' for decoherence in this model.
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"abstract": "Central to many discussion of decoherence is a master equation for the\nreduced density matrix of a massive particle experiencing scattering from its\nsurrounding environment, such as that of Joos and Zeh. Such master equations\nenjoy a close relationship with spontaneous localization models, like the GRW\nmodel. This aim of this paper is to present two derivations of the master\nequation. The first derivation is a pedagogical model designed to illustrate\nthe origins of the master equation as simply as possible, focusing on physical\nprinciples and without the complications of S-matrix theory. This derivation\nmay serve as a useful tutorial example for students attempting to learn this\nsubject area. The second is the opposite: a very general derivation using\nnon-relativistic many body field theory. It reduces to the equation of the type\ngiven by Joos and Zeh in the one-particle sector, but correcting certain\nnumerical factors which have recently become significant in connection with\nexperimental tests of decoherence. This master equation also emphasizes the\nrole of local number density as the ``preferred basis\u0027\u0027 for decoherence in this\nmodel.",
"arxiv_id": "quant-ph/0607132",
"authors": [
"J. J. Halliwell"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1751-8113/40/12/S11",
"title": "Two Derivations of the Master Equation of Quantum Brownian Motion",
"url": "https://arxiv.org/abs/quant-ph/0607132"
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