We investigate numerically the momentum correlations in a two-dimensional, harmonically trapped interacting Bose system at
T=0 temperature, by using a particle number preserving Bogoliubov approximation. Interaction-induced quantum fluctuations of the quasicondensate lead to a large anticorrelation dip between particles of wave numbers
k and $\ensuremath{-}\mathbf{k}$ for $|\mathbf{k}|\ensuremath{\sim}1/{R}_{c}$, with
Rc the typical size of the condensate. The anticorrelation dip found is a clear fingerprint of coherent quantum fluctuations of the condensate. In contrast, for larger wave numbers, $|\mathbf{k}|\ensuremath{\gg}1/{R}_{c}$, a weak positive correlation is found between particles of wave numbers
k and $\ensuremath{-}\mathbf{k}$, in accordance with the Bogoliubov result for homogeneous interacting systems.
Particle fluctuations in mesoscopic Bose systems of arbitrary spatial dimensionality are considered. Both ideal Bose gases and interacting Bose systems are studied in the regions above the Bose–Einstein condensation temperature T c , as well as below this temperature. The strength of particle fluctuations defines whether the system is stable or not. Stability conditions depend on the spatial dimensionality d and on the confining dimension D of the system. The consideration shows that mesoscopic systems, experiencing Bose–Einstein condensation, are stable when: (i) ideal Bose gas is confined in a rectangular box of spatial dimension d > 2 above T c and in a box of d > 4 below T c ; (ii) ideal Bose gas is confined in a power-law trap of a confining dimension D > 2 above T c and of a confining dimension D > 4 below T c ; (iii) the interacting Bose system is confined in a rectangular box of dimension d > 2 above T c , while below T c , particle interactions stabilize the Bose-condensed system, making it stable for d = 3 ; (iv) nonlocal interactions diminish the condensation temperature, as compared with the fluctuations in a system with contact interactions.
Fluctuations of the number of condensed atoms in a finite-size, weakly interacting Bose gas confined in a box potential are investigated for temperatures up to the critical region. The canonical partition functions are evaluated using a recursive scheme for smaller systems, and a saddle-point approximation for larger samples that allows to treat realistic size systems containing up to N ∼10 5 particles. We point out the importance of particle-number constraint and interactions between out of condensate atoms for the statistics near the critical region. For sufficiently large systems, the crossover from the anomalous to normal scaling of the fluctuations is observed. The excitations are described in a self-consistent way within the Bogoliubov-Popov approximation, and the interactions between thermal atoms are described by means of the Hartree-Fock method.