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The partition function and specific heat of a system consisting of a finite number of bosons confined in an external potential are calculated in canonical ensemble. Using the grand partition function as the generating function of the partition function, an iterative scheme is established for the calculation of the partition function of system with an arbitrary number of particles. The scheme is applied to finite number of bosons confined in isotropic and anisotropic parabolic traps and in rigid boxes. The specific heat as a function of temperature is studied in detail for different number of particles, different degrees of anisotropy, and different spatial dimensions. The cusp in the specific heat is taken as an indication of Bose-Einstein condensation (BEC).It is found that the results corresponding to a large number of particles are approached quite rapidly as the number of bosons in the system increases. For large number of particles, results obtained within our iterative scheme are consistent with those of the semiclassical theory of BEC in an external potential based on the grand canonical treatment.
Bose-Einstein condensation (BEC) of an ideal gas is investigated, beyond the thermodynamic limit, for a finite number $N$ of particles trapped in a generic three-dimensional power-law potential. We derive an analytical expression for the condensation
In this reply we show that the criticisms raised by J. Noronha are based on a misapplication of the model we have proposed in [A. Jaouadi, M. Telmini, E. Charron, Phys. Rev. A 83, 023616 (2011)]. Here we explicitly discuss the range of validity of th
The fundamental phenomenon of Bose-Einstein Condensation (BEC) has been observed in different systems of real and quasi-particles. The condensation of real particles is achieved through a major reduction in temperature while for quasi-particles a mec
We report on the attainment of Bose-Einstein condensation with ultracold strontium atoms. We use the 84Sr isotope, which has a low natural abundance but offers excellent scattering properties for evaporative cooling. Accumulation in a metastable stat
We report on the attainment of Bose-Einstein condensation of 86Sr. This isotope has a scattering length of about +800 a0 and thus suffers from fast three-body losses. To avoid detrimental atom loss, evaporative cooling is performed at low densities a