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The possibility to apply phase-space methods to many-body interacting systemsmight provide accurate descriptions of correlations with a reduced numericalcost. For instance, the so--called stochastic mean-field phase-space approach,where the complex dynamics of interacting fermions is replaced by a statisticalaverage of mean-field like trajectories is able to grasp some correlationsbeyond the mean-field. We explore the possibility to use alternative equationsof motion in the phase-space approach. Guided by the BBGKY hierarchy, equationsof motion that already incorporate part of the correlations beyond mean-fieldare employed along each trajectory. The method is called Hybrid Phase-Space(HPS) because it mixes phase-space techniques and the time-dependent reduceddensity matrix approach. The novel approach is applied to the one-dimensionalFermi-Hubbard model. We show that the predictive power is improved compared tothe original stochastic mean-field method. In particular, in the weak-couplingregime, the results of the HPS theory can hardly be distinguished from theexact solution even for long time.

Combining phase-space and time-dependent reduced density matrix approach to describe the dynamics of interacting fermions