Abstract
The analytical probability distributions of thequasi-two-dimensional (quasi-2D) (and purely 2D) ideal andinteracting Bose gases are investigated by using a canonical ensemble approach. Using the analytical probability distribution of the condensate, the statistical properties suchas the mean occupation number and particle number fluctuationsof the condensate are calculated. Research shows that there isa continuous crossover of the statistical properties from a quasi-2D to a purely 2D ideal gas or interacting gas. Incontrast to the case of a 3D Bose gas, the interaction betweenatoms changes, in a deep way, the nature of the particle numberfluctuations.
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