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Teoreticheskaya i Matematicheskaya Fizika, 2018, Volume 196, Number 1, Pages 161–166
DOI: https://doi.org/10.4213/tmf9597
(Mi tmf9597)
 

This article is cited in 1 scientific paper (total in 1 paper)

New formulas related to analytic number theory and their applications in statistical physics

V. P. Maslovab

a National Research University "Higher School of Economics," Moscow, Russia
b Ishlinsky Institute for Problems in Mechanics, RAS, Moscow, Russia
Full-text PDF (384 kB) Citations (1)
References:
Abstract: Since the deep paper by Bohr and Kalckar in 1938, it has been known that the Ramanujan formula in number theory is related to statistical physics and nuclear theory. From the early 1970s, there have been attempts to generalize number theory from the space of integers to the space of rational numbers, i.e., to construct a so-called analytic number theory. In statistical physics, we consider parameters such as the volume $V$, temperature $T$, and chemical potential $\mu$, which are not integers and are consequently related to analytic number theory. This relation to physical concepts leads us to seek new relations in analytic number theory, and these relations turn out to be useful in statistical physics.
Keywords: analytic number theory, Bose–Einstein distribution, Fermi–Dirac distribution, Gentile distribution, self-consistent equation, specific energy jump.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations AAAA-A17-117021310377-1
This research was supported by the Federal Target Program (contract No. AAAA-A17-117021310377-1).
Received: 21.03.2018
English version:
Theoretical and Mathematical Physics, 2018, Volume 196, Issue 1, Pages 1082–1087
DOI: https://doi.org/10.1134/S0040577918070127
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. P. Maslov, “New formulas related to analytic number theory and their applications in statistical physics”, TMF, 196:1 (2018), 161–166; Theoret. and Math. Phys., 196:1 (2018), 1082–1087
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf9597
  • https://doi.org/10.4213/tmf9597
  • https://www.mathnet.ru/eng/tmf/v196/i1/p161
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:696
    Full-text PDF :150
    References:86
    First page:81
     
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