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Mathematical Problems in the Theory of Superconductivity

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Part of the book series: Mathematical Physics Studies ((MPST,volume 17))

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

  1. Bardeen, J., Cooper, L. N., and Schrieffer, J. R. Microscopic theory of superconductivity, Phys. Rev. (1957), 106, 162–164

    Article  MathSciNet  ADS  Google Scholar 

  2. Bardeen, J., Cooper, L. N., and Schrieffer, J. R.Theory of superconductivity, Phys. Rev. (1957), 108, 1175 -1204.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. Belyaev, S. T. Application of the methods of quantum field theory to the system of bosons, Zh. Eksp. Teor. Fiz. (1958), 34, 417–432.

    Google Scholar 

  4. Billard, P. and Fano, G. An existence proof for the gap equation in the superconductivity theory, Comm. Math. Phys. (1968), 10, 274–279.

    MATH  Google Scholar 

  5. 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.

    MathSciNet  Google Scholar 

  6. 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.

    MathSciNet  Google Scholar 

  7. Bogolyubov, N. N. On a new method in the theory of superconductivity. I, Zh. Eksp. Teor. Fiz.(1958), 34, issue 1,58–65.

    Google Scholar 

  8. Bogolyubov, N. N. On a new method in the theory of superconductivity. I, Zh. Eksp. Teor. Fiz.(1958), 34, issue 1,73–79.

    Google Scholar 

  9. 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.

    Google Scholar 

  10. 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.

    Google Scholar 

  11. Bogolyubov, N. N. Superfluidity and quasiaverages in the problems of statistical mechanics, Trudy Mat. Inst. Steklov. (1988), issue 2, 3–45.

    MathSciNet  Google Scholar 

  12. 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.

    Google Scholar 

  13. 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.

    Google Scholar 

  14. Bogolyubov, N. N. (jr.) A Method for Investigating Model Hamiltonians [in Russian], Nauka, Moscow, 1974.

    Google Scholar 

  15. 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.

    Google Scholar 

  16. Haag, R. The mathematical structure of the Bardeen-Cooper-Schrieffer model, Nuovo Cim. (1962), 25, 287.

    Article  MathSciNet  MATH  Google Scholar 

  17. Hugenholtz, N. M. Physica(1957),23,481

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. Hugenholtz, N. M. Quantum theory of many body systems, Reports Progr. Phys. (1965) 28, 201 -248.

    Article  ADS  Google Scholar 

  19. Hugenholtz, N. M. and Pines, D. Ground-state energy and excitation spectrum of a system of interacting bosons, Phys. Rev. (1959), 116, 489–506.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. Khalatnikov, I. M. Theory of Superfluidity [in Russian], Nauka, Moscow, 1971.

    Google Scholar 

  21. Kobe,D.H. Derivation of the principle of compensation of dangerous diagrams, J. Math. Phys. (1967), 8, No. 6, 1200–1210.

    Article  ADS  Google Scholar 

  22. 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.

    Google Scholar 

  23. Petrina, D. Ya. On Hamiltonians in quantum statistics and on a model Hamiltonian in the theory of superconductivity, Teor. Mat. Fiz. (1970), 4, 394.

    Article  MathSciNet  MATH  Google Scholar 

  24. Petrina, D. Ya. and Yatsyshin, V. P. On a model Hamiltonian in the theory of superconductivity, Teor. Mat. Fiz. (1972), 10, 283.

    Article  Google Scholar 

  25. Quaegebeur, J. and Verbeure, A. Relaxation of the ideal Bose gas, Lett. Math. Phys. (1985), 9, 93 -101. Thirring,W.

    Article  MathSciNet  ADS  Google Scholar 

  26. Quaegebeur, J. and Verbeure, A. On the mathematical structure of the BCS model, Comm. Math. Phys. (1968), 7, 181.

    Article  MathSciNet  Google Scholar 

  27. 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.

    Google Scholar 

  28. 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.

    Article  MathSciNet  Google Scholar 

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© 1995 Springer Science+Business Media Dordrecht

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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

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4083-9

  • Online ISBN: 978-94-011-0185-1

  • eBook Packages: Springer Book Archive

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