Gaussian phase-space representation of Fermion dynamics; Beyond the time-dependent-Hartree-Fock approximation

A Gaussian operator representation for the many body density matrix of fermionic systems, developed by Corney and Drummond [Phys. Rev. Lett, v93, 260401 (2004)], is used to derive approximate decoupling schemes for their dynamics. In this approach the reduced single electron density matrix elements serve as stochastic variables which satisfy an exact Fokker-Planck equation. The number of variables scales as ~N^2 rather than ~exp(N) with the basis set size, and the time dependent Hartree Fock approximation (TDHF) is recovered in the "classical" limit. An approximate closed set of equations of motion for the one and two-particle reduced density matrices, provides a direct generalization of the TDHF.