Particle Fluctuations in Mesoscopic Bose 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) 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.