• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site
  • HSE University
  • Publications of HSE
  • Articles
  • Analytical Number Theory and the Energy of Transition of the Bose Gas to the Fermi gas. Critical Lines as Boundaries of the Noninteracting Gas (an Analog of the Bose Gas in Classical Thermodynamics)

Article

Analytical Number Theory and the Energy of Transition of the Bose Gas to the Fermi gas. Critical Lines as Boundaries of the Noninteracting Gas (an Analog of the Bose Gas in Classical Thermodynamics)

Russian Journal of Mathematical Physics. 2018. Vol. 25. No. 2. P. 220-232.

It is proved that the distributions of the analytic number theory coincide with
the Bose–Einstein distribution. The transition of the boson branch of the decomposition of
an integer number (with repeated terms) into the fermion branch (without repeated terms) is
described in detail near a small activity. Analytic formulas for the energy of transition of the
Bose gas to the Fermi gas are obtained in the three-dimensional case and the nine-dimensional
case (diatomic molecule). The radius of the Bose gas “jump” in the transition to the Fermi
gas is calculated. The relationship between the constructed concept and the thermodynamics
is described based on the obtained experimental values of gas characteristics on critical lines.