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## New Insight into the Partition Theory of Integers Related to Problems of Thermodynamics and Mesoscopic Physics

Mathematical notes. 2017. Vol. 102. No. 2. P. 234-251.

It is shown in the paper that the number pN(M) of partitions of a positive integer M

into N positive integer summands coincides with the Bose and Fermi distributions with logarithmic

accuracy if one identifies M with energy and N with the number of particles. We use the Gentile

statistics (a.k.a. parastatistics) to derive self-consistent algebraic equations that enable one to

construct the curves representing the least upper bound and the greatest lower bound of the

repeated limits as M → ∞ and N → ∞. The resulting curves allow one to generalize the notion

of BKT (Berezinskii–Kosterlitz–Thouless) topological phase transition and explaining a number of

phenomena in thermodynamics and mesoscopic physics.

Priority areas:
mathematics

Language:
English

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

Zybin K., Il'yn A. S., Physics-Uspekhi 2016 Vol. 59 No. 12 P. 1241-1244

This paper reviews the statistical properties and calculates the velocity structure functions of flows produced by a large-scale random scaling force in the Burgers model. ...

Added: September 22, 2017

Bespalov P. A., O.N. Savina, Astronomy Letters 2015 Vol. 41 No. 10 P. 601-605

We discuss the connection of the formation and properties of solar atmosphere transition region
characterized by a steep electron temperature gradient with electrostatic turbulence, which provides a high
effective electron collision frequency and a low thermal conductivity of the medium. A simple dependence
of the noise electric field in the transition region on the effective collision frequency has ...

Added: September 30, 2015

49606783, Russian Journal of Mathematical Physics 2019 Vol. 26 No. 3 P. 352-367

In this paper, a new physical notion, intensity, is introduced.
The notion of intensity occurs in a special statistics, known as Gentile statistics, which
is asymptotically close to ordinary thermodynamics. The introduction
of the new notion of intensity in the theory of nuclear matter
essentially changes the thermodynamical picture. Moreover, we can
say that the thermodynamics of nuclear matter is ...

Added: August 25, 2019

49606783, Mathematical notes 2017 Vol. 102 No. 4 P. 533-540

The author attempts to change and supplement the standard scheme of partitions of
integers in number theory to make it completely concur with the Bohr–Kalckar correspondence
principle. In order to make the analogy between the the atomic nucleus and the theory of partitions
of natural numbers more complete, to the notion of defect of mass author assigns the ...

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

49606783, Mathematical notes 2018 Vol. 103 No. 2 P. 316-318

In view of the results obtained in this communication we can connect macroscopy and microscopy via an intermediate level of mesoobjects. ...

Added: December 8, 2018

49606783, Mathematical notes 2014 Vol. 95 No. 5 P. 3-18

In this paper, a new approach to the two-body problem is considered in greater detail than in previous papers of the author.
The semiclassical transition from quantum statistics to classical statistics is studied and an analog of superfluidity
in classical thermodynamics for supercritical states is obtained. ...

Added: December 21, 2014

49606783, Russian Journal of Mathematical Physics 2017 Vol. 24 No. 4 P. 495-504

This paper presents a new approach to thermodynamics based on two “first
principles”: the theory of partitions of integers and Earth gravitation. The self-correlated
equation obtained by the author from Gentile statistics is used to describe the effect of
accumulation of energy at the moment of passage from the boson branch of the partition to
its fermion branch. The ...

Added: November 17, 2018

Kalinin N., Shkolnikov M., Discrete and continuous dynamical systems, A 2018 Vol. 38 No. 6 P. 2827-2849

The theory of tropical series, that we develop here, firstly appeared in the study of the growth of pluriharmonic functions. Motivated by waves in sandpile models we introduce a dynamic on the set of tropical series, and it is experimentally observed that this dynamic obeys a power law. So, this paper serves as a compilation of results ...

Added: April 17, 2018

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

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

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

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

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

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

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

Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83

We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...

Added: November 1, 2019

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

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

Зайцев В. И., Щавелин В. М., М. : ВИНИТИ РАН, 1985

Added: November 30, 2020