# Particle Fluctuations in Mesoscopic Bose Systems

## TL;DR

This paper investigates particle fluctuations in mesoscopic Bose systems across different dimensions and confinement conditions, establishing stability criteria and effects of interactions and trapping potentials on Bose-Einstein condensation.

## Contribution

It provides a comprehensive analysis of stability conditions for mesoscopic Bose systems considering both ideal and interacting cases across various dimensions and trapping geometries.

## Key findings

- Stability depends on spatial and confining dimensions.
- Ideal gases are stable in certain dimensions above and below T_c.
- Interactions can stabilize systems below T_c in three dimensions.

## Abstract

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.