Ideal Bose systems

R.K. Pathria, Paul D. Beale

E.R. Smith, Norman E. Frankel

Raj K. Pathria

Zijun Yan

By introducing the concept of pseudovolume, an ideal Bose gas trapped in a harmonic potential is treated as a free one. This means the equation of state of the trapped system, which has been elusive to date, can be derived and all thermodynamic functions of the system can be expressed in a compact form similar to those of a free ideal Bose system. Thus, a unified description of the two classes of systems is achieved and the internal relation and difference between the thermodynamic properties of the trapped and free ideal Bose systems are further revealed. Moreover, some significant and novel conclusions are obtained.

Raj K. Pathria

Vyacheslav I. Yukalov

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.