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Exact and approximate many-body dynamics with stochastic one-body density matrix evolution

Denis Lacroix
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Abstract

We show that the dynamics of interacting fermions can be exactly replaced by a quantum jump theory in the many-body density matrix space. In this theory, jumps occur between densities formed of pairs of Slater determinants, $D_{ab}=| Φ_a > < Φ_b |$, where each state evolves according to the Stochastic Schrödinger Equation (SSE) given in ref. \cite{Jul02}. A stochastic Liouville-von Neumann equation is derived as well as the associated Bogolyubov-Born-Green-Kirwood-Yvon (BBGKY) hierarchy. Due to the specific form of the many-body density along the path, the presented theory is equivalent to a stochastic theory in one-body density matrix space, in which each density matrix evolves according to its own mean field augmented by a one-body noise. Guided by the exact reformulation, a stochastic mean field dynamics valid in the weak coupling approximation is proposed. This theory leads to an approximate treatment of two-body effects similar to the extended Time-Dependent Hartree-Fock (Extended TDHF) scheme. In this stochastic mean field dynamics, statistical mixing can be directly considered and jumps occur on a coarse-grained time scale. Accordingly, numerical effort is expected to be significantly reduced for applications.

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Denis Lacroix. 2005-07-29. Exact and approximate many-body dynamics with stochastic one-body density matrix evolution. https://doi.org/10.1103/physrevc.71.064322

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