Effectiveaction approach to a trapped Bose gas
Abstract
The effectiveaction 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 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 wellknown Bogoliubov [J. Phys. (Moscow) 11, 23 (1947)] and Popov, (Zh. Éksp. Teor. Fiz. 47, 1759 (1964) [Sov. Phys. JETP 20, 1185 (1965)]) equations are examined analytically for a homogeneous dilute Bose gas and numerically for a gas trapped in a harmonicoscillator potential. The expansion to oneloop order, and hence the Bogoliubov equation, is shown to be valid for the zerotemperature trapped gas as long as the characteristic length of the trapping potential exceeds the swave scattering length.
 Publication:

Physical Review A
 Pub Date:
 September 2002
 DOI:
 10.1103/PhysRevA.66.033607
 arXiv:
 arXiv:condmat/0209121
 Bibcode:
 2002PhRvA..66c3607L
 Keywords:

 03.75.Fi;
 05.30.Jp;
 Boson systems;
 Condensed Matter
 EPrint:
 17 pages, 10 figures, accepted for publication in Phys. Rev. A