Properties of Nambu--Goldstone Bosons in a Single-Component Bose--Einstein Condensate

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We theoretically study the properties of Nambu--Goldstone bosons in an interacting single-component Bose--Einstein condensate (BEC). We first point out that the proofs of Goldstone's theorem by Goldstone et al. [Phys. Rev. 127 (1962) 965] may be relevant to distinct massless modes of the BEC: whereas the first proof deals with the poles of the single-particle Green's function \hat{G}, the second one concerns those of the two-particle Green's function. Thus, there may be multiple Nambu--Goldstone bosons even in the single-component BEC with broken U(1) symmetry. The second mode turns out to have an infinite lifetime in the long-wavelength limit in agreement with the conventional viewpoint. In contrast, the first mode from \hat{G}, i.e., the Bogoliubov mode in the weak-coupling regime, is shown to be a ``bubbling'' mode fluctuating temporally out of and back into the condensate. The substantial lifetime originates from an ``improper'' structure of the self-energy inherent in the BEC, which has been overlooked so far and will be elucidated here, and removes various infrared divergences pointed out previously.
2011-08-15