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Rigorous approach to the problem of ultraviolet divergencies in dilute Bose gases

Maxim Olshanii·Ludovic Pricoupenko
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Abstract

We have found an expression for the full many-body Green's function of N pairwise finite-range interacting atoms, in a form of a chain fraction involving two-body T-matrices only, with no explicit presence of the interaction potentials themselves. We show that in the limit of infinitely small potential range, this expression reduces to the Green's function for N atoms interacting via a generalized pseudo-potential, function of a free parameter Λ. Using this Λ-freedom we resolve all inconsistensies of the Hartree-Fock-Bogoliubov formalism known so far, with no ad hoc modifications of the theory.

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Maxim Olshanii, Ludovic Pricoupenko. 2002-01-11. Rigorous approach to the problem of ultraviolet divergencies in dilute Bose gases. https://doi.org/10.1103/physrevlett.88.010402

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