Accuracy of the time-dependent Hartree-Fock approximation for uncorrelated initial states

Details Accuracy of the time-dependent Hartree-Fock approximation for uncorrelated initial states Accuracy of the time-dependent Hartree-Fock approximation for uncorrelated initial states

2003-11-30

arxiv.org/abs/quant-ph/0312005v1

Physics

Quantum Physics

18 pages. To appear in Journal of Statistical Physics

Scientific paper

10.1023/B:JOSS.0000022381.86923.

This article concerns the time-dependent Hartree-Fock (TDHF) approximation of single-particle dynamics in systems of interacting fermions. We find that the TDHF approximation is accurate when there are sufficiently many particles and the initial many-particle state is any Gibbs equilibrium state for noninteracting fermions (with Slater determinants as a special example). Assuming a bounded two-particle interaction, we obtain a bound on the error of the TDHF approximation, valid for short times. We further show that the error of the TDHF approximation vanishes at all times in the mean field limit.

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