Chaos in Time Dependent Variational Approximations to Quantum Dynamics

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dc.creatorCooper, Fred
dc.creatorDawson, John
dc.creatorHabib, Salman
dc.creatorRyne, Robert D.
dc.date1996-10-09
dc.date1996-10-16
dc.date.accessioned2026-07-07T11:48:32Z
dc.date.available2026-07-07T11:48:32Z
dc.descriptionDynamical 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.
dc.description10 pages (12 figures), RevTeX (plus macro), uses epsf, minor typos corrected
dc.identifierhttps://arxiv.org/abs/quant-ph/9610013
dc.identifierhttp://arxiv.org/abs/quant-ph/9610013
dc.identifierPhys.Rev.E57:1489-1498,1998
dc.identifierdoi:10.1103/PhysRevE.57.1489
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/202950
dc.subjectQuantum Physics
dc.subjectChaotic Dynamics
dc.titleChaos in Time Dependent Variational Approximations to Quantum Dynamics
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