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## НОВЫЕ ФОРМУЛЫ, СВЯЗАННЫЕ С АНАЛИТИЧЕСКОЙ ТЕОРИЕЙ ЧИСЕЛ, И ИХ ПРИЛОЖЕНИЕ К СТАТИСТИЧЕСКОЙ ФИЗИКЕ

Теоретическая и математическая физика. 2018. Т. 196. № 1. С. 161–166.

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 μ, 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.

Priority areas:
mathematics

Language:
Russian

49606783, Mathematical notes 2018 Vol. 103 No. 4 P. 616–620

A relation between the jump of spin and the corresponding jump of energy is derived. This relation is used to determine the binding energy of the nucleus and the “entanglement” energy between two bosons. The latter is shown to be inversely proportional to the area in the two-dimensional case. ...

Added: December 8, 2018

49606783, 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 ...

Added: December 9, 2018

49606783, Mathematical notes 2017 Vol. 102 No. 4 P. 583–586

Added: November 17, 2018

49606783, Mathematical notes 2017 Vol. 101 No. 3 P. 488–496

Abstract—Regularization of the Bose–Einstein distribution using a parastatistical correction,
i.e., by means of the Gentile statistics, is carried out. It is shown that the regularization result
asymptotically coincides with the Erdo˝ s formula obtained by using Ramanujan’s formula for the
number of variants of the partition of an integer into summands. TheHartley entropy regarded as the
logarithm of the ...

Added: October 28, 2018

Chernyshev V. L., Minenkov D. S., Nazaikinskii V. E., / Cornell University. Series math "arxiv.org". 2016. No. 1604.03509.

For any k>1, we find the asymptotics of the counting function of k-th power-free elements in an additive arithmetic semigroup with exponential growth of the abstract prime counting function. This paper continues the authors' earlier research dealing with the case of infinite k. ...

Added: April 13, 2016

Kolokoltsov V., Transactions of the Moscow Mathematical Society 2021 Vol. 82 No. 1 P. 93–104

Combining intuitive probabilistic assumptions with the basic laws of classical thermodynamics, using
the latter to express probabilistic parameters in terms of the thermodynamic quantities, we get a simple
unified derivation of the fundamental ensembles of statistical physics avoiding any limiting procedures,
quantum hypothesis and even statistical entropy maximization. This point of view leads also to some
related classes of ...

Added: October 29, 2021

Kucheryavyy P., / Cornell University. Series arXiv "math". 2022.

Let w(n) be an additive non-negative integer-valued arithmetic function which is equal to 1 on primes. We study the distribution of n+w(n) (mod p) and give a lower bound for the density of the set of numbers which are not representable as n+w(n). ...

Added: October 30, 2022

Maslov V., Mathematical notes 2017 Vol. 101 No. 4 P. 660–665

In the paper “The relationship between the Fermi–Dirac distribution and statistical
distributions in languages” (This issue of “Math. Notes”), the Bose–Einstein and Fermi–Dirac
distributions are considered in connectionwith frequency distributions in languages in the context of
the author’s approach to thermodynamics and number theory problems. The present article presents
certain clarifications of certain notions used in that approach, in ...

Added: October 28, 2018

49606783, Mathematical notes 2018 Vol. 103 No. 6 P. 929–935

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 → 0; in particular, the neighborhood of the ...

Added: December 8, 2018

49606783, Mathematical notes 2017 Vol. 102 No. 6 P. 824–835

The author constructs his thermodynamics on the following two “first principles”: the
partition theory of integers and the notion of Earth gravity. On the basis of number theory,
equivalence classes in mesoscopy and soft condensates in the partition theory of integers are
considered. The self-consistent equation obtained by the author on the basis of Gentile statistics
is used to ...

Added: November 18, 2018

Sergeev A., Васильев А. Ю., Russian Mathematical Surveys 2013 Vol. 68 No. 3 P. 435–502

Teichmüller theory is a ramified and rapidly developing area of mathematics which has multiple connections with other directions in the mathematical sciences and with their applications, first and foremost in mathematical physics. In this survey the main lines of development of this theory and its applications to string theory are presented in a historical context.
Bibliography: 128 titles. ...

Added: April 9, 2015

Пенза: ПГУ, 2015

В сборник трудов включены доклады юбилейного ХХ-го Международного симпозиума «Надежность и качество», проходившего с 25 по 31 мая 2015 г. в городе Пензе.
Рассмотрены актуальные проблемы теории и практики повышения надежности и качества; эффективности внедрения инновационных и информационных технологий в фундаментальных научных и прикладных исследованиях, образовательных и коммуникативных системах и средах, экономике и юриспруденции; методов и ...

Added: May 31, 2015

BOSSY M., Jabir J. M., Electronic Communications in Probability 2018 Vol. 23 P. 1–14

In this paper, we prove a particle approximation, in the sense of the propagation of chaos, of a Lagrangian stochastic model submitted to specular boundary condition and satisfying the mean no-permeability condition. ...

Added: June 7, 2018

Akhmedov E., Physical Review D - Particles, Fields, Gravitation and Cosmology 2013 Vol. 87 No. 4 P. 044049

Following Krotov and Polyakov [ Nucl. Phys. B849 410 (2011)], we show that in global de Sitter space its isometry is broken by the loop IR divergences for any invariant vacuum state of the massive scalars. We derive a kinetic equation in global de Sitter space that follows from the Dyson-Schwinger equation of the Schwinger-Keldysh ...

Added: February 27, 2013

Belavin V., Geiko R., Journal of High Energy Physics 2017 Vol. 125 P. 1–13

We continue to investigate the dual description of the Virasoro conformal blocks arising in the framework of the classical limit of the AdS3/CFT2 correspondence. To give such an interpretation in previous studies, certain restrictions were necessary. Our goal here is to consider a more general situation available through the worldline approximation to the dual AdS gravity. ...

Added: August 31, 2017

Буров А.А., Герман А. Д., Косенко И. И., Космические исследования 2014 Т. 52 № 4 С. 307–312

The problem of planar oscillations of a pendulum with variable length suspended on the Moon’s surface is considered. It is assumed that the Earth and Moon (or, in the general case, a planet and its satellite, or an asteroid and a spacecraft) revolve around the common center of mass in unperturbed elliptical Keplerian orbits. We ...

Added: November 8, 2014

Gorsky A., Valba O. V., Journal of Complex Networks 2020 Vol. 8 No. 1 P. cnaa008

In this article, we show numerically the strong finite-size effects in exponential random graphs. Particularly, for the two-star model above the critical value of the chemical potential for triplets a ground state is a star-like graph with the finite set of hubs at network density p<0.5p<0.5 or as the single cluster at p>0.5p>0.5. We find that there exists ...

Added: August 28, 2020

М.: Издательство математико-механического факультета МГУ, 2009

В настоящий сборник вошли аннотации докладов участников XVI международной конференции «Ломоносов» по секции «Математика и механика». ...

Added: February 4, 2013

Окубо Ю. undefined., Journal of Physics: Conference Series 2017 Vol. 804 No. 012036 P. 1–8

We investigate the existence and the orthogonality of the generalized Jack symmetric functions which play an important role in the AGT relations. We show their orthogonality by deforming them to the generalized Macdonald symmetric functions. ...

Added: October 26, 2017

49606783, Russian Journal of Mathematical Physics 2019 Vol. 26 No. 2 P. 168–173

The parameters of unstable short-living isotopes are studied from
the mathematical point of view. The values of the chemical potential
and activity parameters that determine the neutron halo arising when
the neutron separates from the nucleus of an unstable isotope are
calculated. The analogy between nuclear physics and economics is
considered from the point of view of such parameters as ...

Added: August 25, 2019

Kurkina O. E., Kurkin A. A., Rouvinskaya E. et al., Письма в Журнал экспериментальной и теоретической физики 2012 Т. 95 № 2 С. 98–103

Nonlinear wave dynamics is discussed using the extended modified Korteweg–de Vries equation that includes the combination of the third- and fifth- order terms and is valid for waves in a three-layer fluid with so-called symmetric stratification. The derived equation has solutions in the form of solitary waves of various polarities. At small amplitudes, they are ...

Added: August 24, 2012

Aseeva N., Gromov E., Onosova I. V. et al., JETP Letters 2016 Vol. 103 No. 10 P. 653–657

Evolution of solitons is addressed in the framework of a third-order nonlinear Schrödinger equation (NLSE), including nonlinear dispersion, third-order dispersion and a pseudo-stimulated-Raman-scattering (pseudo-SRS) term, i.e., a spatial-domain counterpart of the SRS term, which is well known as a part of the temporal domain NLSE in optics. In this context, it is induced by the ...

Added: June 28, 2016

Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1–16915-18

Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...

Added: November 16, 2020

Budkov Y., Journal of Physics: Condensed Matter 2019 Vol. 31 P. 078002–078003

We reply to the comment on our paper by Budkov (2018 J. Phys.: Condens. Matter 30 344001). ...

Added: January 4, 2019