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

TL;DR

This paper develops a Gaussian phase-space method for fermion dynamics that extends the time-dependent Hartree-Fock approximation by deriving stochastic equations for reduced density matrices, enabling more efficient simulations.

Contribution

It introduces a Gaussian operator representation for fermionic systems that generalizes TDHF through approximate decoupling schemes and stochastic equations for density matrices.

Findings

Number of variables scales as N^2, improving computational efficiency.

Derivation of a closed set of equations extending TDHF.

Provides a framework for more accurate fermion dynamics simulations.

Abstract

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.