Bose–Einstein Condensation as a Deposition Phase Transition of Quantum Hard Spheres and New Relations between Bosonic and Fermionic Pressures


  • К.А. Bugaev Bogolyubov Institute for Theoretical Physics, Taras Shevchenko National University of Kyiv, Department of Physics
  • O.I. Ivanytskyi Bogolyubov Institute for Theoretical Physics, CFisUC, Department of Physics, University of Coimbra
  • B.E. Grinyuk Bogolyubov Institute for Theoretical Physics
  • I.P. Yakimenko Department of Physics, Chemistry and Biology (IFM), Link¨oping University



quantum gases, Van der Waals, equation of state, statistical multifragmentation model, Bose–Einstein condensation, deposition phase transition


We investigate the phase transition of Bose–Einstein particles with the hard-core repulsion in the grand canonical ensemble within the Van der Waals approximation. It is shown that the pressure of non-relativistic Bose–Einstein particles is mathematically equivalent to the pressure of simplified version of the statistical multifragmentation model of nuclei with the vanishing surface tension coefficient and the Fisher exponent тF = 5/2 , which for such parameters has the 1-st order phase transition. The found similarity of these equations of state allows us to show that within the present approach the high density phase of Bose-Einstein particles is a classical macro-cluster with vanishing entropy at any temperature which, similarly to the system of classical hard spheres, is a kind of solid state. To show this we establish new relations which allow us to identically represent the pressure of Fermi–Dirac particles in terms of pressures of Bose–Einstein particles of two sorts.


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How to Cite

Bugaev К., Ivanytskyi, O., Grinyuk, B., & Yakimenko, I. (2020). Bose–Einstein Condensation as a Deposition Phase Transition of Quantum Hard Spheres and New Relations between Bosonic and Fermionic Pressures. Ukrainian Journal of Physics, 65(11), 963.



Fields and elementary particles