dorsal/arxiv
View SchemaQuantum noise and stochastic reduction
| Authors | Dorje C. Brody, Lane P. Hughston |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0508217 |
| URL | https://arxiv.org/abs/quant-ph/0508217 |
| DOI | 10.1088/0305-4470/39/4/008 |
| Journal | Journal of Physics A39, 833-876 (2006) |
Abstract
In standard nonrelativistic quantum mechanics the expectation of the energy is a conserved quantity. It is possible to extend the dynamical law associated with the evolution of a quantum state consistently to include a nonlinear stochastic component, while respecting the conservation law. According to the dynamics thus obtained, referred to as the energy-based stochastic Schrodinger equation, an arbitrary initial state collapses spontaneously to one of the energy eigenstates, thus describing the phenomenon of quantum state reduction. In this article, two such models are investigated: one that achieves state reduction in infinite time, and the other in finite time. The properties of the associated energy expectation process and the energy variance process are worked out in detail. By use of a novel application of a nonlinear filtering method, closed-form solutions--algebraic in character and involving no integration--are obtained for both these models. In each case, the solution is expressed in terms of a random variable representing the terminal energy of the system, and an independent noise process. With these solutions at hand it is possible to simulate explicitly the dynamics of the quantum states of complicated physical systems.
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"abstract": "In standard nonrelativistic quantum mechanics the expectation of the energy\nis a conserved quantity. It is possible to extend the dynamical law associated\nwith the evolution of a quantum state consistently to include a nonlinear\nstochastic component, while respecting the conservation law. According to the\ndynamics thus obtained, referred to as the energy-based stochastic Schrodinger\nequation, an arbitrary initial state collapses spontaneously to one of the\nenergy eigenstates, thus describing the phenomenon of quantum state reduction.\nIn this article, two such models are investigated: one that achieves state\nreduction in infinite time, and the other in finite time. The properties of the\nassociated energy expectation process and the energy variance process are\nworked out in detail. By use of a novel application of a nonlinear filtering\nmethod, closed-form solutions--algebraic in character and involving no\nintegration--are obtained for both these models. In each case, the solution is\nexpressed in terms of a random variable representing the terminal energy of the\nsystem, and an independent noise process. With these solutions at hand it is\npossible to simulate explicitly the dynamics of the quantum states of\ncomplicated physical systems.",
"arxiv_id": "quant-ph/0508217",
"authors": [
"Dorje C. Brody",
"Lane P. Hughston"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/39/4/008",
"journal_ref": "Journal of Physics A39, 833-876 (2006)",
"title": "Quantum noise and stochastic reduction",
"url": "https://arxiv.org/abs/quant-ph/0508217"
},
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