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We present a strategy for mapping the dynamics of a fermionic quantum systemto a set of classical dynamical variables. The approach is based on imposingthe correspondence relation between the commutator and the Poisson bracket,preserving Heisenberg's equation of motion for one-body operators. In order toaccommodate the effect of two-body terms, we further impose quantization on thespin-dependent occupation numbers in the classical equations of motion, with aparameter that is determined self-consistently. Expectation values forobservables are taken with respect to an initial quasiclassical distributionthat respects the original quantization of the occupation numbers. The proposedclassical map becomes complete under the evolution of quadratic Hamiltoniansand is extended for all even order observables. We show that the map providesan accurate description of the dynamics for an interacting quantum impuritymodel in the coulomb blockade regime, at both low and high temperatures. Thenumerical results are aided by a novel importance sampling scheme that employsa reference system to reduce significantly the sampling effort required toconverge the classical calculations.

A complete quasiclassical map for the dynamics of interacting fermions