Abstract
In this chapter, we give an exposition of the basic ideas in the theory of superconductivity which describes the phenomenon of electric resistance vanishing at low temperatures. For years, this phenomenon was only observed at temperatures close to absolute zero but recent discoveries of superconductivity in metalloceramics have raised the upper bound to the temperatures of liquid nitrogen.
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References
Bardeen, J., Cooper, L. N., and Schrieffer, J. R. Microscopic theory of superconductivity, Phys. Rev. (1957), 106, 162–164
Bardeen, J., Cooper, L. N., and Schrieffer, J. R.Theory of superconductivity, Phys. Rev. (1957), 108, 1175 -1204.
Belyaev, S. T. Application of the methods of quantum field theory to the system of bosons, Zh. Eksp. Teor. Fiz. (1958), 34, 417–432.
Billard, P. and Fano, G. An existence proof for the gap equation in the superconductivity theory, Comm. Math. Phys. (1968), 10, 274–279.
Bogolyubov, N. N. To the theory of superfluidity, Izv. Akad. Nauk SSSR., Ser. Fiz. (1947), 11,No. 1, 77–90; see also: Selected Papers [in Russian], Vol. 2, Naukova Dumka,Kiev (1970), pp. 210-224.
Bogolyubov, N. N. Energy levels of a nonideal Bose - Einstein gas, Vestnik Mosk. Univ. (1947),No. 7, 43–56; see also: Selected Papers [in Russian], Vol. 2, Naukova Dumka,Kiev (1970), pp. 242-257.
Bogolyubov, N. N. On a new method in the theory of superconductivity. I, Zh. Eksp. Teor. Fiz.(1958), 34, issue 1,58–65.
Bogolyubov, N. N. On a new method in the theory of superconductivity. I, Zh. Eksp. Teor. Fiz.(1958), 34, issue 1,73–79.
Bogolyubov, N. N. On the Model Hamiltonian in the Theory of Superconductivity [in Russian], Preprint JINR, No. R-511, Dubna, 1960; see also: Selected Papers [in Russian],Vol. 3, Naukova Dumka, Kiev (1970), pp. 110 -173.
Bogolyubov, N. N. Quasiaverages in the Problems of Statistical Mechanics [in Russian], Preprint JINR, No. R-1451, Dubna, 1963.; see also: Selected Papers [in Russian], Vol. 3,Naukova Dumka, Kiev (1970), pp. 174-243.
Bogolyubov, N. N. Superfluidity and quasiaverages in the problems of statistical mechanics, Trudy Mat. Inst. Steklov. (1988), issue 2, 3–45.
Bogolyubov, N. N., Tolmachev, V. V., and Shirkov, D. V. A New Method in the Theory of Superconductivity [in Russian], Izd. Akad. Nauk SSSR, Moscow, 1958.
Bogolyubov, N. N., Zubarev, D. N., and Tserkovnikov, Yu. A. An asymptotically exact solution for the model Hamiltonian in the theory of superconductivity, Zh. Eksp. Teor. Fiz. (1960), 39, issue 1, 120–129.
Bogolyubov, N. N. (jr.) A Method for Investigating Model Hamiltonians [in Russian], Nauka, Moscow, 1974.
Bogolyubov, N. N. (jr.), Brankov, J. G., Zagrebnov, V. A., Kurbatov, A. M., and Tonchev, N. S. The Method of Approximating Hamiltonian in Statistical Physics [in Russian], Izd. Bolgar. Akad. Nauk, Sofia, 1981.
Haag, R. The mathematical structure of the Bardeen-Cooper-Schrieffer model, Nuovo Cim. (1962), 25, 287.
Hugenholtz, N. M. Physica(1957),23,481
Hugenholtz, N. M. Quantum theory of many body systems, Reports Progr. Phys. (1965) 28, 201 -248.
Hugenholtz, N. M. and Pines, D. Ground-state energy and excitation spectrum of a system of interacting bosons, Phys. Rev. (1959), 116, 489–506.
Khalatnikov, I. M. Theory of Superfluidity [in Russian], Nauka, Moscow, 1971.
Kobe,D.H. Derivation of the principle of compensation of dangerous diagrams, J. Math. Phys. (1967), 8, No. 6, 1200–1210.
Lewis, J. T. Why do bosons condense?, in: Statistical Mechanics and Field Theory: Mathematical Aspects. (Proceedings, Groningen, 1985; T. C. Dorlas, N. M. Hugenholtz, and M. Winnink (eds.)), Springer Lect. Notes Phys. (1986), 257.
Petrina, D. Ya. On Hamiltonians in quantum statistics and on a model Hamiltonian in the theory of superconductivity, Teor. Mat. Fiz. (1970), 4, 394.
Petrina, D. Ya. and Yatsyshin, V. P. On a model Hamiltonian in the theory of superconductivity, Teor. Mat. Fiz. (1972), 10, 283.
Quaegebeur, J. and Verbeure, A. Relaxation of the ideal Bose gas, Lett. Math. Phys. (1985), 9, 93 -101. Thirring,W.
Quaegebeur, J. and Verbeure, A. On the mathematical structure of the BCS model, Comm. Math. Phys. (1968), 7, 181.
Van den Berg, M., Lewis, J. T., and Pule, J. V. A general theory of Bose - Einstein condensation, Helv. Phys. Acta. (1968), 59, 1271–1288.
Zagrebnov, V. A. and Papoyan, V. V. On the problem of equivalence of ensembles for Bose systems (the ideal Bose gas), Teor. Mat. Fiz. (1986) 69, 1–22.
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Petrina, D.Y. (1995). Mathematical Problems in the Theory of Superconductivity. In: Mathematical Foundations of Quantum Statistical Mechanics. Mathematical Physics Studies, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0185-1_4
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DOI: https://doi.org/10.1007/978-94-011-0185-1_4
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