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Quantum Monte-Carlo methods and exact treatment of the two-body problem with Hartree-Fock Bogoliubov states

Denis Lacroix
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Abstract

In this article, we show that the exact two-body problem can be replaced by quantum jumps between densities written as $D=| Ψ_a \right> \left< Ψ_b |$ where $| Ψ_a \right>$ and $| Ψ_b \right>$ are vacuum for different quasi-particles operators. It is shown that the stochastic process can be written as a Stochastic Time-Dependent Hartree-Fock Bogoliubov theory (Stochastic TDHFB) for the generalized density ${\cal R}$ associated to $D$ where ${\cal R}^2 = {\cal R}$ along each stochastic trajectory.

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Denis Lacroix. 2006-05-16. Quantum Monte-Carlo methods and exact treatment of the two-body problem with Hartree-Fock Bogoliubov states. https://arxiv.org/abs/nucl-th/0605033

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