Auxiliary field approach to dilute Bose gases with tunable interactions

Details Auxiliary field approach to dilute Bose gases with tunable interactions Auxiliary field approach to dilute Bose gases with tunable interactions

2011-05-25

arxiv.org/abs/1105.4932v1

Phys.Rev.A83:053622,2011

Physics

Condensed Matter

Quantum Gases

16 pages, 7 figures

Scientific paper

10.1103/PhysRevA.83.053622

We rewrite the Lagrangian for a dilute Bose gas in terms of auxiliary fields related to the normal and anomalous condensate densities. We derive the loop expansion of the effective action in the composite-field propagators. The lowest-order auxiliary field (LOAF) theory is a conserving mean-field approximation consistent with the Goldstone theorem without some of the difficulties plaguing approximations such as the Hartree and Popov approximations. LOAF predicts a second-order phase transition. We give a set of Feynman rules for improving results to any order in the loop expansion in terms of composite-field propagators. We compare results of the LOAF approximation with those derived using the Popov approximation. LOAF allows us to explore the critical regime for all values of the coupling constant and we determine various parameters in the unitarity limit.

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