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arXiv:quant-ph/0407036

Exact Stochastic Reformulation of Non-Relativistic Quantum Dynamics

Murat Çetinbaş, Joshua Wilkie

Published Jul 5, 2004• 0 citations
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Abstract

We show that any non-relativistic quantum N-body dynamics problem with pairwise interactions can be exactly reformulated in terms of N well behaved 1-body stochastic density equations. Specifically, the time evolving N-body density matrix is written as an average of tensor products of 1-body densities each of which obeys a stochastic evolution equation. Such decompositions can be constructed for any mixture of fermions and bosons. The evolution equations for the 1-body densities preserve norm, Hermiticity and positivity.

DOI
10.48550/arxiv.quant-ph/0407036

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We show that any non-relativistic quantum N-body dynamics problem with pairwise interactions can be exactly reformulated in terms of N well behaved 1-body stochastic density equations. Specifically, the time evolving N-body density matrix is written as an average of tensor products of 1-body densities each of which obeys a stochastic evolution equation. Such decompositions can be constructed for any mixture of fermions and bosons. The evolution equations for the 1-body densities preserve norm, Hermiticity and positivity.
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We investigate a reformulation of the dynamics of interacting fermion systems in terms of a stochastic extension of time-dependent Hartree-Fock equations. From a path-integral representation of the evolution operator, we show that the exact N-body state can be interpreted as a coherent average over Slater determinants evolving in a random mean-field. The imaginary time propagation is also presented and gives a similar scheme which converges to the exact ground state. In addition, the growth of statistical errors is examined to show the stability of this stochastic formulation.
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