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Effective-action approach to a trapped Bose gas

Emil Lundh·Jorgen Rammer
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Abstract

The effective-action formalism is applied to a gas of bosons. The equations describing the condensate and the excitations are obtained using the loop expansion for the effective action. For a homogeneous gas the Beliaev expansion in terms of the diluteness parameter is identified in terms of the loop expansion. The loop expansion and the limits of validity of the well-known Bogoliubov and Popov equations are examined analytically for a homogeneous dilute Bose gas and numerically for a gas trapped in a harmonic-oscillator potential. The expansion to one-loop order, and hence the Bogoliubov equation, is shown to be valid for the zero-temperature trapped gas as long as the characteristic length of the trapping potential exceeds the s-wave scattering length.

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Emil Lundh, Jorgen Rammer. 2002-09-05. Effective-action approach to a trapped Bose gas. https://doi.org/10.1103/physreva.66.033607

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