Abstract
@Dynamical chaos has recently been shown to exist in the Gaussian approximation in quan-tum mechanics and in the self-consistent mean field approach to studying the dynamics ofquantum fields. In this study, we first show that any variationalapproximationto the dynam-ics of a quantum system based on the Dirac action principle leads to a classical Hamiltoniandynamics for the variational parameters. Since this Hamiltonian is generically nonlinearand nonintegrable, the dynamics thus generated can be chaotic, in distinction to the exactquantum evolution. We then restrict attention to a system of two biquadratically coupledquantum oscillators and study two variational schemes, the leading order large N (fourcanonical variables) and Hartree (six canonical variables) approximations. The chaos seenin the approximate dynamics is an artifact of the approximations: this is demonstrated bythe fact that its onset occurs on the same characteristic time scale as the breakdown of theapproximations when compared to numerical solutions of the time-dependent Schr¨odingerequation.PACS numbers: 05.45. +b, 03.65. Sq, 2.30 Wd, 03.65 -w
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