dorsal/arxiv
View SchemaRelaxation of quantum states under energy perturbations
| Authors | Dorje Brody, Lane Hughston, Joanna Syroka |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0208073 |
| URL | https://arxiv.org/abs/quant-ph/0208073 |
| DOI | 10.1098/rspa.2003.1113 |
| Journal | Proceedings of the Royal Society London 459, 2297-2316 (2003) |
Abstract
The energy-based stochastic extension of the Schrodinger equation is perhaps the simplest mathematically rigourous and physically plausible model for the reduction of the wave function. In this article we apply a new simulation methodology for the stochastic framework to analyse formulae for the dynamics of a particle confined to a square-well potential. We consider the situation when the width of the well is expanded instantaneously. Through this example we are able to illustrate in detail how a quantum system responds to an energy perturbation, and the mechanism, according to the stochastic evolutionary law, by which the system relaxes spontaneously into one of the stable eigenstates of the Hamiltonian. We examine in particular how the expectation value of the Hamiltonian and the probability distribution for the position of the particle change in time. An analytic expression for the typical timescale of relaxation is derived. We also consider the small perturbation limit, and discuss the relation between the stochastic framework and the quantum adiabatic theorem.
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"abstract": "The energy-based stochastic extension of the Schrodinger equation is perhaps\nthe simplest mathematically rigourous and physically plausible model for the\nreduction of the wave function. In this article we apply a new simulation\nmethodology for the stochastic framework to analyse formulae for the dynamics\nof a particle confined to a square-well potential. We consider the situation\nwhen the width of the well is expanded instantaneously. Through this example we\nare able to illustrate in detail how a quantum system responds to an energy\nperturbation, and the mechanism, according to the stochastic evolutionary law,\nby which the system relaxes spontaneously into one of the stable eigenstates of\nthe Hamiltonian. We examine in particular how the expectation value of the\nHamiltonian and the probability distribution for the position of the particle\nchange in time. An analytic expression for the typical timescale of relaxation\nis derived. We also consider the small perturbation limit, and discuss the\nrelation between the stochastic framework and the quantum adiabatic theorem.",
"arxiv_id": "quant-ph/0208073",
"authors": [
"Dorje Brody",
"Lane Hughston",
"Joanna Syroka"
],
"categories": [
"quant-ph"
],
"doi": "10.1098/rspa.2003.1113",
"journal_ref": "Proceedings of the Royal Society London 459, 2297-2316 (2003)",
"title": "Relaxation of quantum states under energy perturbations",
"url": "https://arxiv.org/abs/quant-ph/0208073"
},
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