Abstract
We investigate the particle-number fluctuations due to the collective excitations created in a two-dimensional (2D) and a quasi-2D Bose-Einstein condensates (BECs) at low temperature. We find that the fluctuations display an anomalous behavior, i.e., for the 2D BEC they are proportional to ${N}^{2},$ where N is the total number of particles. For the quasi-2D BEC, the particle-number fluctuations are proportional not only to ${N}^{2}$ but also to the square root of the trapping frequency in the strongly confined direction.
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