
Mat. Zametki, 2018, Volume 103, Issue 6, paper published in the English version journal
(Mi mz12096)




This article is cited in 2 scientific papers (total in 2 papers)
Papers published in the English version of the journal
Statistical Transition of Bose Gas to Fermi Gas
V. P. Maslov^{ab} ^{a} Ishlinsky Institute for Problems in Mechanics,
Russian Academy of Sciences, Moscow, Russia
^{b} National Research University Higher School of Economics, Moscow, Russia
Abstract:
It is well known that the formula for the Fermi distribution is obtained
from the formula for the Bose distribution if the argument of the polylogarithm, the activity $a$,
the energy, and the number of particles
change sign.
The paper deals with the behavior of the Bose–Einstein distribution
as
$a\to 0$;
in particular, the neighborhood of the point
$a=0$
is studied in great detail,
and the expansion of both the Bose distribution
and the Fermi distribution
in powers of the parameter $a$
is used.
During the transition from the Bose distribution
to the Fermi distribution, the principal term of the distribution
for the specific energy undergoes a jump
as
$a\to 0$.
In this paper, we find the value of the parameter $a$,
close to zero, but not equal to zero,
for which the Bose distribution (in the statistical sense)
becomes zero.
This allows us to find the point $a$,
distinct from zero,
at which a jump of the specific energy occurs.
Using the value of the number of particles on the caustic,
we can obtain the jump of the total energy of the Bose system
to the Fermi system.
Near the value
$a=0$,
the author uses Gentile statistics,
which makes it possible to study the transition
from the Bose statistics to the the Fermi statistics in great detail.
Here an important role is played
by the selfconsistent equation obtained by the author earlier.
Keywords:
Bose statistics, Fermi statistics, Gentile statistics,
jump of specific energy, selfconsistent equation.
English version:
Mathematical Notes, 2018, 103:6, 929–935
Bibliographic databases:
Received: 27.04.2018
Language:
Citation:
V. P. Maslov, “Statistical Transition of Bose Gas to Fermi Gas”, Math. Notes, 103:6 (2018), 929–935
Citation in format AMSBIB
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\by V.~P.~Maslov
\paper Statistical Transition of Bose Gas to Fermi Gas
\jour Math. Notes
\yr 2018
\vol 103
\issue 6
\pages 929935
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\crossref{https://doi.org/10.1134/S0001434618050292}
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Linking options:
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Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:

V. P. Maslov, “Analytical number theory and the energy of transition of Bose gas to Fermi gas. Critical lines as boundaries of noninteracting gas (an analog of the Bose gas in classical thermodynamics)”, Russ. J. Math. Phys., 25:2 (2018), 220–232

V. P. Maslov, “New formulas related to analytic number theory and their applications in statistical physics”, Theoret. and Math. Phys., 196:1 (2018), 1082–1087

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