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A study of an interacting system of bosons in a ring trap at a finite temperature is presented. We consider a gas with contact and long-range dipolar interactions within a framework of the classical fields approximation. For a repulsive gas we have obtained coherence length, population of the ground state and its fluctuations as a function of temperature. In the case of an attractive gas we study local density fluctuations. Additionally, we exactly calculate the partition function for the ideal gas in the canonical ensemble and derive several other macroscopic state functions.

We study the statistical properties of a gas of interacting bosons trapped in a box potential in two and three dimensions. Our primary focus is the characteristic temperature Tp, i.e., the temperature at which the fluctuations of the number of condensed atoms (or, in 2D, the number of motionless atoms) are maximal. Using the Fock state sampling method, we show that Tp increases due to interaction. In 3D, this temperature converges to the critical temperature in the thermodynamic limit. In 2D, we show the general applicability of the method by obtaining a generalized dependence of the characteristic temperature on the interaction strength. Finally, we discuss the experimental conditions necessary for the verification of our theoretical predictions. topics: Bose-Einstein condensate, statistical ensembles, quantum gases