Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chaos in Time Dependent Variational Approximations to Quantum Dynamics   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.

37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics