Regular and irregular behavior of trajectories in the time-dependent Hartree-Fock approximation.

Abstract

We investigate the validity of the time-dependent Hartree-Fock (TDHF) approximation for a finite fermion model system. With the help of coherent states we derive equations of motion for the one-particle density, which are of classical Hamiltonian form and can be interpreted in terms of generalized coordinates and momenta. The corresponding trajectories in phase space show transitions between regular and chaotic regimes depending on the parameters of the model. A chaotic behavior indicates a failure of the TDHF approximation because the exact solutions are always regular due to the linearity of the Schr\"odinger equation.