dorsal/arxiv
View SchemaChaos in Time Dependent Variational Approximations to Quantum Dynamics
| Authors | Fred Cooper, John Dawson, Salman Habib, Robert D. Ryne |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9610013 |
| URL | https://arxiv.org/abs/quant-ph/9610013 |
| DOI | 10.1103/PhysRevE.57.1489 |
| Journal | Phys.Rev.E57:1489-1498,1998 |
Abstract
Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first show that any variational approximation to the dynamics of a quantum system based on the Dirac action principle leads to a classical Hamiltonian dynamics for the variational parameters. Since this Hamiltonian is generically nonlinear and nonintegrable, the dynamics thus generated can be chaotic, in distinction to the exact quantum evolution. We then restrict attention to a system of two biquadratically coupled quantum oscillators and study two variational schemes, the leading order large N (four canonical variables) and Hartree (six canonical variables) approximations. The chaos seen in the approximate dynamics is an artifact of the approximations: this is demonstrated by the fact that its onset occurs on the same characteristic time scale as the breakdown of the approximations when compared to numerical solutions of the time-dependent Schrodinger equation.
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"abstract": "Dynamical chaos has recently been shown to exist in the Gaussian\napproximation in quantum mechanics and in the self-consistent mean field\napproach to studying the dynamics of quantum fields. In this study, we first\nshow that any variational approximation to the dynamics of a quantum system\nbased on the Dirac action principle leads to a classical Hamiltonian dynamics\nfor the variational parameters. Since this Hamiltonian is generically nonlinear\nand nonintegrable, the dynamics thus generated can be chaotic, in distinction\nto the exact quantum evolution. We then restrict attention to a system of two\nbiquadratically coupled quantum oscillators and study two variational schemes,\nthe leading order large N (four canonical variables) and Hartree (six canonical\nvariables) approximations. The chaos seen in the approximate dynamics is an\nartifact of the approximations: this is demonstrated by the fact that its onset\noccurs on the same characteristic time scale as the breakdown of the\napproximations when compared to numerical solutions of the time-dependent\nSchrodinger equation.",
"arxiv_id": "quant-ph/9610013",
"authors": [
"Fred Cooper",
"John Dawson",
"Salman Habib",
"Robert D. Ryne"
],
"categories": [
"quant-ph",
"chao-dyn",
"nlin.CD"
],
"doi": "10.1103/PhysRevE.57.1489",
"journal_ref": "Phys.Rev.E57:1489-1498,1998",
"title": "Chaos in Time Dependent Variational Approximations to Quantum Dynamics",
"url": "https://arxiv.org/abs/quant-ph/9610013"
},
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