Exact results on the two-particle Green's function of a Bose-Einstein condensate

TL;DR

This paper derives an exact expression for the two-particle Green's function in an interacting Bose-Einstein condensate, revealing that its poles differ from those of the single-particle Green's function, challenging previous assumptions.

Contribution

It provides a new exact formula for the two-particle Green's function incorporating self-energies and vertices, clarifying its spectral properties.

Findings

Poles of the two-particle Green's function are not shared with the single-particle Green's function.

The derived formula facilitates approximate calculations of the two-particle Green's function.

Contradicts previous studies regarding the relation of poles between two-particle and single-particle Green's functions.

Abstract

Starting from the Dyson-Beliaev and generalized Gross-Pitaevskii equations with an extra nonlocal potential, we derive an exact expression of the two-particle Green's function K for an interacting Bose-Einstein condensate in terms of unambiguously defined self-energies and vertices. The formula can be a convenient basis for approximate calculations of K. It also tells us that poles of K are not shared with (i.e. shifted from) those of the single-particle Green's function, contrary to the conclusion of previous studies.