Abstract
In the theory of superfluidity and superconductivity, a jump of the free energy was discovered theoretically and was naturally called a zeroth-order phase transition. We present an example of an exactly solvable problem in which such a phase transition occurs.
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REFERENCES
R. Kubo, Thermodynamics North-Holland Publ.Company, Amsterdam, 1970.
L.L. Landau and E.M. Lifshits, Quantum Mechanics [in Russian], Gostekhizdat, Moscow, 1948.
V.P. Maslov, “Mathematical aspects of the theory of weakly nonideal Bose and Fermi gases on a crystal basis,” Funktsional. Anal. i Prilozhen. [Functional Anal. Appl.], 37 (2003), no. 2, 16–27.
V.P. Maslov,“ Geometric “quantization ”of thermodynamics and statistical corrections at critical oints,” Teoret. Mat. Fiz. [Theoret. and Math. Phys.], 101 (1994), no.3, 433–441.
V.P. Maslov,“ Axioms of nonlinear averaging in nancial mathematics and the dynamics of stock price,” Teor. Veroyatnost. i Primenen. [Theory Probab. Appl.], 48 (2003), no. 4, 799–810.
N.N. Bogolyubov, Selected Works in Three Volumes [in Russian ], vols. 1, 2, Naukova Dumka, Kiev, 1970.
V.P. Maslov, S.A. Molchanov, and A.Ya. Gordon, “Behavior of generalized eigenfunctions at infinity and Schrödinger conjecture,” Russ. J. Math. Phys. 1 (1993), no. 1, 71–104.
N.N. Bogolyubov, “To the theory of superfluidity,” Izv. Akad. Nauk SSSR Ser. Fiz. 11 (1947), no. 1, 77–90.
V.P. Maslov, “Axioms of nonlinear averaging in nancial mathematics and an analog of phase transitions,” Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.], 393 (2003), no. 6, 735–739.
V.P. Maslov, Thermodynamics Quantization and Ultra-Secondary Quantization [in Russian ], Institute for Computer Studies, Moscow, 2001.
V.P. Maslov, “A new representation of the Hamiltonian operator for bosons and fermions.Quantization of the free energy and the dependence of the Landau criterion on the temperature,” Mat. Zametki [Math. Notes], 68 (2000), no. 6, 945–947.
V.P. Maslov and O.Yu. Shvedov, The Complex Germ Method in Many-Particle Problem and Quantum Field Theory [in Russian ], Editorial URSS, Moscow, 2000.
V.P. Maslov, “Analytic extension of asymptotic formulas and axiomatics of thermodynamics and quasithermodynamics,” Funktsional. Anal. i Prilozhen. [Functional Anal. Appl.], 28 (1994), no.4, 28–41.
V.P. Maslov, “Model of a weakly nonideal Bose gas.Phase transition in the superfluid state and the spouting effect,” Vestnik Moskov. Univ. Ser. III Fiz. Astronom. [Moscow Univ. Phys. Bull.] (2003), no. 1, 3–5.
V.P. Maslov, “Two-level model of a weakly nonideal Bose gas.Phase transition in a metastable (superfluid)state,” Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.], 389 (2003), no. 4, 468–469.
V.P. Maslov, “On a weakly nonideal Bose gas model leading to the s outing effect,” Teoret. Mat. Fiz. [Theoret. and Math. Phys.], 135 (2003), no. 3, 524–528.
V.P. Maslov, “Bose gas phase transitions in the two-zone crystal model.The thermodynamic effect,” Uspekhi Mat.NaukRussian Math. Surveys, 58 (2003), no.2 (350), 157–158.
V.P. Maslov, “On a model of high-temperature superconductivity,” Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.], 391 (2003), no. 5, 605–609.
V.P. Maslov, “On a model of high-temperature superconductivity,” Mat. Zametki [Math. Notes], 73 (2003), no. 6, 942–946.
V.P. Maslov, “A new exactly solvable model of high-temperature superconductivity,” Russ. J. Math. Phys. 11 no. 2, 199–208.
V.P. Maslov, “On an exactly solvable model of low-temperature superconductivity,” Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.], 397 (2003), no.6, 1–3.
V.P. Maslov, “Exact model of high-temperature superconductivity,” Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.], 398 (2004), no. 3.
V.P. Maslov, “Repulsion taken into account in the model of high-temperature conductivity and superfluidity of a Bose gas on a crystal basis.The zeroth-order phase transition,” Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.], 398 (2004), no. 6.
V.P. Maslov, “On an exactly solvable model of superfluidity,” Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.], 399 (2004), no.1.
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Maslov, V.P. Zeroth-Order Phase Transitions. Mathematical Notes 76, 697–710 (2004). https://doi.org/10.1023/B:MATN.0000049669.32515.f0
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DOI: https://doi.org/10.1023/B:MATN.0000049669.32515.f0