Effect of the Zero-Mode on the Response of a Trapped Bose-Condensed Gas

The dynamical response of a trapped Bose-Einstein condensate (BEC) is formulated consistently with quantum field theory and is numerically evaluated. We regard the BEC as a manifestation of the breaking of the global phase symmetry. Then, the Goldstone theorem implies the existence of a zero energy excitation mode (the zero-mode). We calculate the effect of the zero-mode on the response frequency and show that the contribution of the zero-mode to the first excitation mode is not so important in the parameter set realized in the existing experiment. This is the reason that experimental results can be described using the Bogoliubov prescription, although it breaks the consistency of the description in quantum field theory.Comment: 18 pages, 3 figure

Dynamical Origin of Power Spectra

We discuss a possible origin of Tsallis' statistics from the correlation among constituents which reduces the phase space of the system. We also show that in the system of coupled linear harmonic oscillators can exhibit a Tsallis type behavior.Comment: 22 pages, 7 figures, prepared for the European Physical Journal A - Hadrons and Nucle