نبذة مختصرة : 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&ndash
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&ndash
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 >
(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.
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