dorsal/arxiv
View SchemaWeisskopf-Wigner Decay Theory for the Energy-Driven Stochastic Schr\"odinger Equation
| Authors | Stephen L. Adler |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0208123 |
| URL | https://arxiv.org/abs/quant-ph/0208123 |
| DOI | 10.1103/PhysRevD.67.025007 |
Abstract
We generalize the Weisskopf-Wigner theory for the line shape and transition rates of decaying states to the case of the energy-driven stochastic Schr\"odinger equation that has been used as a phenomenology for state vector reduction. Within the standard approximations used in the Weisskopf-Wigner analysis, and assuming that the perturbing potential inducing the decay has vanishing matrix elements within the degenerate manifold containing the decaying state, the stochastic Schr\"odinger equation linearizes. Solving the linearized equations, we find no change from the standard analysis in the line shape or the transition rate per unit time. The only effect of the stochastic terms is to alter the early time transient behavior of the decay, in a way that eliminates the quantum Zeno effect. We apply our results to estimate experimental bounds on the parameter governing the stochastic effects.
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"abstract": "We generalize the Weisskopf-Wigner theory for the line shape and transition\nrates of decaying states to the case of the energy-driven stochastic\nSchr\\\"odinger equation that has been used as a phenomenology for state vector\nreduction. Within the standard approximations used in the Weisskopf-Wigner\nanalysis, and assuming that the perturbing potential inducing the decay has\nvanishing matrix elements within the degenerate manifold containing the\ndecaying state, the stochastic Schr\\\"odinger equation linearizes. Solving the\nlinearized equations, we find no change from the standard analysis in the line\nshape or the transition rate per unit time. The only effect of the stochastic\nterms is to alter the early time transient behavior of the decay, in a way that\neliminates the quantum Zeno effect. We apply our results to estimate\nexperimental bounds on the parameter governing the stochastic effects.",
"arxiv_id": "quant-ph/0208123",
"authors": [
"Stephen L. Adler"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevD.67.025007",
"title": "Weisskopf-Wigner Decay Theory for the Energy-Driven Stochastic Schr\\\"odinger Equation",
"url": "https://arxiv.org/abs/quant-ph/0208123"
},
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