dorsal/arxiv
View SchemaEffective Theories of Coupled Classical and Quantum Variables from Decoherent Histories: A New Approach to the Backreaction Problem
| Authors | J. J. Halliwell |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9705005 |
| URL | https://arxiv.org/abs/quant-ph/9705005 |
| DOI | 10.1103/PhysRevD.57.2337 |
| Journal | Phys. Rev. D 57, 2337 (1998) |
Abstract
We use the decoherent histories approach to quantum theory to derive the form of an effective theory describing the coupling of classical and quantum variables. The derivation is carried out for a system consisting of a large particle coupled to a small particle with the important additional feature that the large particle is also coupled to a thermal environment producing the decoherence necessary for classicality. The effective theory is obtained by tracing out both the environment and the small particle variables. It consists of a formula for the probabilities of a set of histories of the large particle, and depends on the dynamics and initial quantum state of the small particle. It has the form of an almost classical particle coupled to a stochastic variable whose probabilities are determined by a formula very similar to that given by quantum measurement theory for continuous measurements of the small particle's position. The effective theory gives intuitively sensible answers when the small particle is in a superposition of localized states.
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"abstract": "We use the decoherent histories approach to quantum theory to derive the form\nof an effective theory describing the coupling of classical and quantum\nvariables. The derivation is carried out for a system consisting of a large\nparticle coupled to a small particle with the important additional feature that\nthe large particle is also coupled to a thermal environment producing the\ndecoherence necessary for classicality. The effective theory is obtained by\ntracing out both the environment and the small particle variables. It consists\nof a formula for the probabilities of a set of histories of the large particle,\nand depends on the dynamics and initial quantum state of the small particle. It\nhas the form of an almost classical particle coupled to a stochastic variable\nwhose probabilities are determined by a formula very similar to that given by\nquantum measurement theory for continuous measurements of the small particle\u0027s\nposition. The effective theory gives intuitively sensible answers when the\nsmall particle is in a superposition of localized states.",
"arxiv_id": "quant-ph/9705005",
"authors": [
"J. J. Halliwell"
],
"categories": [
"quant-ph",
"gr-qc"
],
"doi": "10.1103/PhysRevD.57.2337",
"journal_ref": "Phys. Rev. D 57, 2337 (1998)",
"title": "Effective Theories of Coupled Classical and Quantum Variables from Decoherent Histories: A New Approach to the Backreaction Problem",
"url": "https://arxiv.org/abs/quant-ph/9705005"
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