THE ANALYSIS OF NAMBU-GOLDSTONE MODE IN TRAPPED BOSE-EINSTEIN CONDENSATES

Abstract

We analyze the Nambu-Goldstone (NG) mode for a system of trapped Bose-Einstein condensation (BEC). The NG mode is a discrete mode in our case, contrary to the homogeneous case in which the NG mode is in a continuum labeled by a momentum index. In order to control the NG mode, an infinitesimal symmetry-breaking term is introduced. This breaking term plays the role of infinitesimal magnetic field in spin system which fixes the macroscopic "direction" of spin. We calculate a tadpole diagram to evaluate fluctuation effects, taking account of the NG mode, then find that the coefficient of the wave function of condensation is infrared divergent while the remaining terms are finite.