Many-body T-matrix of a two-dimensional Bose-Einstein condensate within the Hartree-Fock-Bogoliubov formalism

TL;DR

This paper develops a finite-temperature many-body T-matrix for a two-dimensional Bose-Einstein condensate using the Hartree-Fock-Bogoliubov formalism, addressing the effects of reduced dimensionality on atomic collisions.

Contribution

It introduces a gapless Hartree-Fock-Bogoliubov approach to compute the many-body T-matrix at finite temperatures in 2D BECs, including a semi-classical renormalization to handle divergences.

Findings

Finite-temperature T-matrix results are obtained within the HFB formalism.

Comparison with other approaches highlights differences in scattering parameters.

The method effectively removes ultra-violet divergences in the calculations.

Abstract

In a two-dimensional Bose-Einstein condensate the reduction in dimensionality fundamentally influences collisions between the atoms. In the crossover regime from three to two dimensions several scattering parameters have been considered. However, finite temperature results are more difficult to obtain. In this work we present the many-body T-matrix at finite temperatures within a gapless Hartree-Fock-Bogoliubov approach and compare to zero and finite temperature results obtained using different approaches. A semi-classical renormalization method is used to remove the ultra-violet divergence of the anomalous average.