Thermodynamic properties of a finite Bose gas in a harmonic trap |
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Authors: | Wang Jian-Hui and Ma Yong-Li |
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Institution: | Department of Physics, Fudan University, Shanghai 200433, China |
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Abstract: | We have investigated the thermodynamic behaviour of ideal
Bose gases with an arbitrary number of particles confined in a
harmonic potential. By taking into account the conservation of total
number $N$ of particles and using a saddle-point approximation, we
derive analytically the simple explicit expression of mean
occupation number in any state of the finite system. The temperature
dependence of the chemical potential, specific heat, and condensate
fraction for the trapped finite-size Bose system is obtained
numerically. We compare our results with the usual treatment which
is based on the grand canonical ensemble. It is shown that there
exists a considerable difference between them at sufficiently low
temperatures, specially for the relative small numbers of Bose
atoms. The finite-size scaling at the transition temperature for the
harmonically trapped systems is also discussed. We find that the
scaled condensate fractions for various system sizes and
temperatures collapse onto a single scaled form. |
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Keywords: | trapped finite bosons simple explicit distribution law thermodynamics finite-size scaling |
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