On the Features of Ideal Bose-Gas Thermodynamic Prop-erties at a Finite Particle Number


  • A.I. Bugrij Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
  • V.M. Loktev Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”




ideal Bose-gas, Bose-distribution, canonical ensembles


The paper is devoted to the theory of an ideal Bose-gas with a finite number N of particles. The exact expressions for the partition functions and occupation numbers of the model in the grand canonical, canonical, and microcanonical ensembles are found. From the calculations, it is followed that, oppositely to the accepted opinion that the chemical potential μ of an ideal Bose-gas is only negative, it can take values in the range −∞ < μ < ∞. The asymptotic expressions (in the case N ≫ 1) for the partition functions and occupation numbers for all above-mentioned thermodynamic ensembles are also evaluated.


L.D. Landau, E.M. Lifshitz. Statistical Physics (Pergamon Press, 1980).

K. Huang. Statistical Mechanics (Wiley, 1987) [ISBN: 0-471-81518-7].

A. Isihara. Statistical Physics (Acad. Press, 1971) [ISBN: 978-1483241012].

N.N. Bogolyubov. Selected Works (Naukova Dumka, 1970), Vol. 2, p. 351.

M.H. Anderson, J.R. Ensher, M.R. Vatthews, C.E. Wieman, E.A. Cornell. Observation of Bose-Einstein condensation in a dilute atomic vapor. Science 269, 198 (1995).


K. Burnett, M. Edwards, C.W. Clark. The theory of Bose-Einstein condensation of dilute gases. Physics Today 52, 37 (12) (1999).


Y. Shin, M. Saba, A. Schirotzek, T.A. Pasquini, A.E. Leanhardt, D.E. Prithard, W. Kttterle. Distillation of Bose-Einstein condensates in a double-well potential. Phys. Rev. Lett. 92, 150401 (2004).


G.K. Chaudhary, A. Chattopadhyay, R. Ramakumar. Bose-Einstein condensate in a quartic potential: Static and dynamic properties. Int. J. Mod. Phys. B 25, 3927 (2012).


W. Ketterlee, N.J. van Druten. Bose-Einstein condensation of a finite number of particles trapped in one or three dimensions. Phys. Rev. A 54, 656 (1996).


S. Grossmann, M. Holthaus. From number theory to statistical mechanics: Bose-Einstein condensation in isolated traps. Chaos, Solitons and Fractals 10, No. 4-5, 795 (1999).


A. Jaouadi, M.Telmini, E.Charron. Bose-Einstein condensation with a finite number of particles in a power-law trap. Phys. Rev. A 83, 023616 (2011); arXiv:1011.6477v2[condmat.quant-gas].


A.I. Bugrij, V.M. Loktev. On the theory of ideal Bose-gas. Low Temperature Physics 47, No. 2, 132 (2021).





How to Cite

Bugrij, A., & Loktev, V. (2022). On the Features of Ideal Bose-Gas Thermodynamic Prop-erties at a Finite Particle Number. Ukrainian Journal of Physics, 67(4), 235. https://doi.org/10.15407/ujpe67.4.235



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