| Recent experiments with ultracold atom gases and pump-probe laser spectroscopy of solids motivate the development of new methods for simulating the dynamics of interacting many-body systems in more than one dimension. The main challenge of this task lies in a systematic reduction of the full quantum dynamics in Hilbert space to a computable approximation, i.e. solving it within a restricted subclass of approximative quantum states. A simple example is the class of Gaussian states (quasifree states) which can be defined as ground states of quadratic Hamiltonians. Although this class does not include all quantum correlations it can describe mean-field phenomena, BCS pairing, nonlinear Gross-Pitaevskij dynamics etc. in an ab initio approach. I will introduce the Gaussian states approximation and present a formalism which models the nonequilibrium dynamics of Hamiltonians with both bosonic and fermionic degrees of freedoms. First results will be discussed. |
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