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Mathematical Theory of Noble Gases
Ch. 6. P. 197-219.
We single out the main features of the mathematical theory of noble gases. It is proved that the points of degeneracy of the Bose gas fractal dimension in momentum space coincide with the critical points of noble gases, while the jumps of the critical indices and the Maxwell rule are related to tunnel quantization in thermodynamics. We consider semiclassical methods for tunnel quantization in thermodynamics as well as those for second and ultrasecond quantization (the creation and annihilation operators for pairs of particles). Each noble gas is associated with a new critical point of the limit negative pressure. The negative pressure is equivalent to covering the (P,Z)- diagram by the second sheet.
In book
Maslov V., Baddiredy A., Aoki Y., Nakada Y., Su M., Kozhemyakin G. N., Szalmas L. Vol. 21. , NY : Nova Science Publishers, 2014
Maslov V., Baddiredy A., Aoki Y. et al., NY : Nova Science Publishers, 2014
We single out the main features of the mathematical theory of noble gases. It is proved that the points of degeneracy of the Bose gas fractal dimension in momentum space coincide with the critical points of noble gases, while the jumps of the critical indices and the Maxwell rule are related to tunnel quantization in ...
Added: November 18, 2013
49606783, Mathematical notes 2010 Vol. 87 No. 5 P. 728-737
The well-known empiric Van der Waals equation contains two constants characterizing a given gas, so that, in general, it depends on the characteristic interaction of particles of the given gas. In this paper, equations depending on three defining constants, are constructed on the basis of he mathematically rigorous results obtained by the author in recent ...
Added: April 13, 2012
Кузнецов Е. А., Kagan M., Теоретическая и математическая физика 2020 Т. 202 № 3 С. 458-473
In the framework of the Gross-Pitaevsky equation, we consider the problem of the expansion of quantum gases into vacuum, for which the chemical potential μ depends on the density n in a power manner with the index v =2/D, where D is the dimension of space. For gas condensates of Bose-atoms at temperatures T → 0 the main ...
Added: February 4, 2020
Kalmynin A. B., Konyagin S., / Cornell University. Series math "arxiv.org". 2023. No. 2303.14833.
Added: November 22, 2023
Kondo S., Chida M., Yamuchi T., K-Theory 2014 Vol. 14 No. 2 P. 313-342
We compute the rational K_2 group of an elliptic surface over a finite field in terms of the order of zeros of the associated L-function. ...
Added: March 15, 2015
Kulakovskii V D, Demenev A. A., Brichkin A. S. et al., Physical Review B: Condensed Matter and Materials Physics 2018 Vol. 98 No. 20 P. 205424-1-205424-6
The dynamics of a pure low polariton (LP) system created by resonant broadband excitation in a wide range of wave vectors was investigated in a high-Q GaAs-based microcavity. The LP system is shown to inherit the high spatial coherence from the laser pulse and does not lose it during decay. As a result, its dynamics ...
Added: January 9, 2019
Demenev A. A., Grishina Y. V., Novikov S. I. et al., Physical Review B: Condensed Matter and Materials Physics 2016 Vol. 94 No. 19 P. 195302-1-195302-8
Time evolution of long-range spatial coherence in a freely decaying cavity-polariton condensate excited resonantly in a high-Q GaAs microcavity is found to be qualitatively different from that in nonresonantly excited condensates. The first-order spatial correlation function g(1)(r1,r2) in response to resonant 1.5 ps pump pulses at normal incidence leaving the exciton reservoir empty is found to be nearly ...
Added: February 15, 2018
Maslov V., Теоретическая и математическая физика 2013 Т. 175 № 1 С. 93-131
We systematically present a new approach to classical thermodynamics using asymptotic distributions from number theory that generalize the Bose-Einstein distribution. We justify the transition to the liquid state, the thermodynamics of fluids, and also the behavior of liquids in the region of negative pressures. We present a comparison with experimental data. ...
Added: November 18, 2013
Dmitriev A., Dmitriev V., Silchev V., WSEAS Transactions on Business and Economics 2017 Vol. 14 No. 33 P. 311-321
This paper proposes a nonlinear dynamical model of stock market. Dynamical variables of the model are the variation of ask and bid price relative to equilibrium values and difference between numbers of market agents in a-state and p-state. A particular market agent being in a-state has maximum amount of valuable information about financial asset and ...
Added: November 24, 2017
Kondo S., Yasuda S., / Cornell University. Series math "arxiv.org". 2014.
We study the homology and the Borel-Moore homology with coefficients in Q of a quotient (called arithmetic quotient) of the Bruhat-Tits building of PGL of a nonarchimedean local field of positive characteristic by an arithmetic subgroup (a special case of the general definition in Harder's article (Invent.\ Math.\ 42, 135-175 (1977)). We define an analogue ...
Added: December 11, 2014
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
Zatelepin A., Shchur L., / Cornell University. Series "Working papers by Cornell University". 2010. No. 1008.3573.
We report on numerical investigation of fractal properties of critical interfaces in two-dimensional Potts models. Algorithms for finding percolating interfaces of Fortuin-Kasteleyn clusters, their external perimeters and interfaces of spin clusters are presented. Fractal dimensions are measured and compared to exact theoretical predictions. ...
Added: March 7, 2016
49606783, Mathematical notes 2013 Vol. 93 No. 1-2 P. 102-136
In this paper we systematically present a new approach to classical thermodynamics, using asymptotic distribution from number theory and generalizing the Bose-Einstein distribution. The phase transition from gas to liquid, the thermodynamics of fluids, as well as the behavior of liquids under negative pressure are elucidated. ...
Added: April 1, 2013
49606783, Mathematical notes 2016 Vol. 100 No. 3 P. 413-420
A parallel between physical derivation and mathematical proof in classical thermodynamics is drawn. A relationship between thermodynamics and analytic number theory is demonstrated. ...
Added: December 7, 2016
Maslov V., Маслова Т. В., Теория вероятностей и ее применения 2013 Т. 57 № 3 С. 443-466
The order statistics and the empirical mathematical expectation (also called the estimate of mathematical expectation in the literature) are considered in the case of infinitely increasing random variables. The Kolmogorov concept which he used in the theory of complexity and the relationship with thermodynamics which was pointed out already by Poincar\'e are considered. We compare ...
Added: November 18, 2013
49606783, Dobrokhotov S. Y., Nazaikinskii V. E., Mathematical notes 2016 Vol. 100 No. 5 P. 828-834
We develop the recent research [1] and introduce the notions of volume and entropy in abstract analytic number theory. The introduction of negative numbers in the generalized partition problem, together with the meaning of such a generalization in some applications of the theory, is discussed. ...
Added: February 21, 2017
Maslov V., Russian Journal of Mathematical Physics 2013 Vol. 20 No. 1 P. 68-101
In the first part of the paper, we introduce the concept of observable quantities associated with a macroinstrument measuring the density and temperature and with a microinstrument determining the radius of a molecule and its free path length, and also the relationship between these observable quantities. The concept of the number of degrees of freedom, ...
Added: November 18, 2013
Menshutin A. Y., Shchur L., Computer Physics Communications 2011 Vol. 182 P. 1819-1823
Two-dimensional structures grown with Witten and Sander algorithm are investigated. We analyze clusters grown off-lattice and clusters grown with antenna method with Nfp=3,4,5,6,7 and 8 allowed growth directions. With the help of variable probe particles technique we measure fractal dimension of such clusters D(N) as a function of their size N . We propose that in the thermodynamic limit of ...
Added: March 25, 2014
Idrisova V. A., Tokareva N. N., Gorodilova A. A. et al., Prikladnaya Diskretnaya Matematika 2023 No. 62 P. 29-54
Every year the International Olympiad in Cryptography Non-Stop University CRYPTO (NSUCRYPTO) offers mathematical problems for university and school students and, moreover, for professionals in the area of cryptography and computer science. The main goal of NSUCRYPTO is to draw attention of students and young researchers to modern cryptography and raise awareness about open problems in ...
Added: March 19, 2024
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
Demenev A. A., Grishina Y. V., Larionov A. V. et al., Physical Review B: Condensed Matter and Materials Physics 2017 Vol. 96 No. 15 P. 155308-1-155308-10
We address polarization instability in a freely decaying polariton condensate created by 2-ps-long linearly polarized laser pulses in the upper sublevel of the lower-polariton (LP) branch in a GaAs-based microcavity with reduced symmetry. The generated linearly polarized condensate is found to lose its stability at excitation densities above the threshold value: it passes into the ...
Added: February 15, 2018
Dmitriev A., Kornilov V., Maltseva S. V., Complexity 2018 Vol. 2018 No. Article ID 4732491 P. 1-11
Recent developments in nonlinear science have caused the formation of a new paradigm called the paradigm of complexity. The self-organized criticality theory constitutes the foundation of this paradigm. To estimate the complexity of a microblogging social network, we used one of the conceptual schemes of the paradigm, namely, the system of key signs of complexity ...
Added: November 24, 2018
Maslov V., Mathematical notes 2012 Vol. 91 No. 5 P. 697-703
We study the case where the values of random variables increase without bound. ...
Added: January 17, 2013
Gromov D., Toikka A., Entropy 2020 Vol. 22 No. 10 P. 1113
In this contribution, we carry on with the research program initiated in J. Math. Chem., 58(6), 2020. Using the methods from geometric thermodynamics, we formally derive and analyze different conditions for thermodynamic stability and determine the limits of their use. In particular, we study, in detail, several versions of the Le Chatelier—Brown principle and demonstrate their ...
Added: October 31, 2020