CHAOS IN TIME-DEPENDENT VARIATIONAL APPROXIMATIONS TO QUANTUM DYNAMICS

Dynamical chaos has recently been shown to exist in the Gaussian appro ximation in quantum mechanics and in the self-consistent mean held app roach to studying the dynamics of quantum fields. In this study, we fi rst note that any variational approximation to the dynamics of a quant um system based on the Dirac action principle leads to a classical Ham iltonian dynamics for the variational parameters. Since this Hamiltoni an is generically nonlinear and nonintegrable, the dynamics thus gener ated can be chaotic, in distinction to the exact quantum evolution. We then restrict our attention to a system of two biquadratically couple d quantum oscillators and study two variational schemes, the leading o rder large-N (four canonical variables) and Hartree (six canonical var iables) approximations. The chaos seen in the approximate dynamics is an artifact of the approximations: this is demonstrated by the fact th at its onset occurs on the same characteristic time scale as the break down of the approximations when compared to numerical solutions of the time-dependent Schrodinger equation. [S1063-651X(98)04301-3].