Here, a dichotomy of particles and waves is employed in a quantum Monte Carlo calculation of interacting electrons. Through the creation and propagation of concurrent stochastic ensembles of walkers in physical space and in Hilbert space, one can correctly predict the ground state and the real-time evolution of a single electron interacting with a larger quantum system. It is shown that such walker ensembles can be constructed straightforwardly through a stochastic sampling (windowing) applied to the mean-field approximation. Our calculations reveal that the ground state and the real-time evolution of the probability distributions and the decoherence due to the Coulomb interaction in the presence of strong ultrashort laser pulses can be accounted for correctly by calculating the density matrix of the electron, without referencing the quantum many-body state of the whole system.
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