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 Funktsional. Anal. i Prilozhen., 2003, Volume 37, Issue 2, Pages 16–27 (Mi faa145)

This article is cited in 22 scientific papers (total in 22 papers)

Mathematical Aspects of Weakly Nonideal Bose and Fermi Gases on a Crystal Base

V. P. Maslov

M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: We consider mathematical aspects of ideal Bose and Fermi gases on a crystal lattice and give a simple model of superfluidity and superconductivity for nonideal Bose and Fermi gases.

Keywords: thermodynamics, Bose gas, Fermi gas, Schrödinger equation, phase transition, Lifshits potential, metastable state, superfluidity

DOI: https://doi.org/10.4213/faa145

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English version:
Functional Analysis and Its Applications, 2003, 37:2, 94–102

Bibliographic databases:

UDC: 517.9
Received: 13.03.2003

Citation: V. P. Maslov, “Mathematical Aspects of Weakly Nonideal Bose and Fermi Gases on a Crystal Base”, Funktsional. Anal. i Prilozhen., 37:2 (2003), 16–27; Funct. Anal. Appl., 37:2 (2003), 94–102

Citation in format AMSBIB
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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:
1. V. P. Maslov, “On a Model of High-Temperature Superconductivity”, Math. Notes, 73:6 (2003), 889–894
2. Maslov V.P., “Axioms of nonlinear averaging in financial mathematics and an analogue of phase transition”, Dokl. Math., 68:3 (2003), 426–429
3. Maslov V.P., “Approximation probabilities, the law of a quasi-stable market, and a phase transition from the “condensate” state”, Dokl. Math., 68:2 (2003), 266–270
4. Maslov A.V.P., “On a model of high-temperature superconductivity”, Doklady Mathematics, 68:1 (2003), 140–144
5. V. P. Maslov, “Zeroth-Order Phase Transitions”, Math. Notes, 76:5 (2004), 697–710
6. V. P. Maslov, “An Exactly Solvable Superfluidity Model and the Phase Transition of the Zeroth Kind (Fountain Effect)”, Theoret. and Math. Phys., 141:3 (2004), 1686–1697
7. Maslov V.P., “Quasistable economics and its relationship to the thermodynamics of superfluids. Default as a zero order phase transition”, Russ. J. Math. Phys., 11:3 (2004), 308–334
8. Maslov V.P., “Taking account of repulsion for a model of high-temperature conductivity and superfluidity of a Bose gas on a crystal substrate: Phase transition of zeroth kind”, Dokl. Math., 70:2 (2004), 822–826
9. Maslov V.P., “An exactly solvable model of low-temperature superconductivity”, Dokl. Math., 70:1 (2004), 648–650
10. Maslov V.P., “A new exactly solvable model of high-temperature superconductivity”, Russ. J. Math. Phys., 11:2 (2004), 199–208
11. Maslov V.P., “Quasistable economics and its relationship to the thermodynamics of superfluids. Default as a zero order phase transition”, Russ. J. Math. Phys., 11:4 (2004), 429–455
12. Maslov V.P., “An exactly solvable model of superfluidity”, Dokl. Math., 70:3 (2004), 966–970
13. Maslov V.P., “On the superfluidity of classical liquid in nanotubes. I. Case of even number of neutrons”, Russ. J. Math. Phys., 14:3 (2007), 304–318
14. V. P. Maslov, “Taking parastatistical corrections to the Bose–Einstein distribution into account in the quantum and classical cases”, Theoret. and Math. Phys., 172:3 (2012), 1289–1299
15. Maslov V.P., “Bose Condensate in the D-Dimensional Case, in Particular, for D=2”, Russ. J. Math. Phys., 19:3 (2012), 317–323
16. Maslov V.P., “A Bose Condensate in the $D$-Dimensional Case, in Particular, for $D=2$ and 1”, Dokl. Math., 86:2 (2012), 700–703
17. V. P. Maslov, “Bose–Einstein-Type Distribution for Nonideal Gas. Two-Liquid Model of Supercritical States and Its Applications”, Math. Notes, 94:2 (2013), 231–237
18. V. P. Maslov, “On New Ideal (Noninteracting) Gases in Supercritical Thermodynamics”, Math. Notes, 97:1 (2015), 85–99
19. Maslov V.P., “Distribution Corresponding To Classical Thermodynamics”, Phys. Wave Phenom., 23:2 (2015), 81–95
20. Maslov V.P., “On Mathematical Investigations Related to the Chernobyl Disaster”, Russ. J. Math. Phys., 25:3 (2018), 309–318
21. Maslov V.P., “Numeration as a Factor Relating the Quantum and Classical Mechanics of Ideal Gases”, Russ. J. Math. Phys., 25:4 (2018), 525–530
22. Chetverikov V.M., “The Spatial Distribution of Magnetization in a Ferromagnetic Semiconductor Thin Film”, Mosc. Univ. Phys. Bull., 73:6 (2018), 592–598
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