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Properties of Nambu-Goldstone Bosons in a Single-Component Bose-Einstein Condensate
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. {\bf
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
, 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 , 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.Comment: 9 pages, 6 gigure