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

Abstract

In this article, we show that the exact two-body problem can be replaced by quantum jumps between densities written as D=| \Psi_a \right> \left< \Psi_b | where | \Psi_a \right> and | \Psi_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 $\mathcal{R}$ associated to $D$ where ${\mathcal{R}}^2=\mathcal{R}$ along each stochastic trajectory.

Comments: 5 pages