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Collective Modes in BCS-Like Models

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Abstract

The Hamiltonian of the gapped modes in the BCS model of superconductivity is derived using the nilpotency expansion. It has the form of the Bogoliubov Hamiltonian of a boson superfluid. The gapped modes have a quadratic dispersion law. The smallest energy gap is smaller than twice the fermionic energy gap. The nilpotency expansion respects all the symmetries and it has been previously applied to nuclear physics and relativistic field theories including QCD. In particular, it reproduces exactly the bosonization occurring in a relativistic 4-fermion interaction model.

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References

  1. Bardeen, J., Cooper, L.N., Schrieffer, J.R.: Phys. Rev. 108, 1175 (1957)

    Article  ADS  MathSciNet  Google Scholar 

  2. Bogoliubov, N.N, Tolmachev, V.V., Shirkov, D.V.: A New Method in The Theory of Superconductivity. Consultants Bureau Inc., New York (1959)

    Google Scholar 

  3. Anderson, P.W.: Phys. Rev. 112, 1900 (1958)

    Article  ADS  MathSciNet  Google Scholar 

  4. Nambu, Y.: Phys. Rev. 117, 648 (1960)

    Article  ADS  MathSciNet  Google Scholar 

  5. Tsuneto, T.: Phys. Rev. 118, 1029 (1960)

    Article  ADS  Google Scholar 

  6. Bardasis, A., Schrieffer, J.R.: Phys. Rev. 121, 1050 (1961)

    Article  ADS  Google Scholar 

  7. See the review, Pekker, D., Varma, C.M.: Annu. Rev. Condens. Matter Phys. 6, 269 (2015)

    Article  ADS  Google Scholar 

  8. Podolsky, D., Sachdev, S.: Phys. Rev. B 86, 054508 (2012)

    Article  ADS  Google Scholar 

  9. Gazit, S., Podolsky, D., Auerbach, A.: Phys. Rev. Lett. 110, 140401 (2013)

    Article  ADS  Google Scholar 

  10. Rancon, A., Dupuis, N.: Phys. Rev. B 89, 180501(R) (2014)

    Article  ADS  Google Scholar 

  11. Cea, T., Castellani, C., Seibold, G., Benfatto, L.: Phys. Rev. Lett. 115, 157002 (2015)

    Article  ADS  Google Scholar 

  12. Caracciolo, S., Laliena, V., Palumbo, F.: JHEP02, 034, [arXiv:hep-lat/0611012v1] (2007)

  13. Wilson, K.G.: Phys. Rev. D 7, 2911 (1973)

    Article  ADS  MathSciNet  Google Scholar 

  14. Palumbo, F.: Phys. Rev. C 72, 14303 (2005)

    Article  ADS  Google Scholar 

  15. Palumbo, F.: Ann. Phys. 324, 2226 (2009)

    Article  ADS  Google Scholar 

  16. Palumbo, F.: J. Supercond. Nov. Magn. 29, 707 (2016)

    Article  Google Scholar 

  17. Caracciolo, S., Palumbo, F., Viola, G.: Ann. Phys. 324, 584 (2009)

    Article  ADS  Google Scholar 

  18. Palumbo, F.: Phys. Rev. D 78, 0145514 (2008)

    Article  Google Scholar 

  19. Caracciolo, S., Palumbo, F.: Phys. Rev. D 85, 094009 (2012)

    Article  ADS  Google Scholar 

  20. Luscher, M.: Comm. Math. Phys. 54, 283 (1977)

    Article  ADS  MathSciNet  Google Scholar 

  21. Bussmann-Holder, A., Kohler, J., Simon, A., Whangbo, M.-H., Bianconi, A., Perali, A.: Condens. Matter 2, 24 (2017). https://doi.org/10.3390/conmat2030024

    Article  Google Scholar 

  22. Nielsen, H.B., Chada, S.: Nucl. Phys. B 105, 445 (1976)

    Article  ADS  Google Scholar 

  23. Kapustin, A: arXiv:120/.945/v2 [hep-ph] 5 (2012)

  24. Watanabe, H., Murayama, H.: arXiv:1203.0609v3 [hep-th] (2012)

  25. Sauls, J.A., Mizushima, T.: Phys. Rev. B 95, 094515 (2017)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

I thank A. Bianconi for interesting conversations about recent developments in superconductivity.

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  1. INFN – Laboratori Nazionali di Frascati, P. O. Box 13, 00044, Frascati, Italy

    Fabrizio Palumbo

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  1. Fabrizio Palumbo
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Correspondence to Fabrizio Palumbo.

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Palumbo, F. Collective Modes in BCS-Like Models. J Supercond Nov Magn 31, 625–629 (2018). https://doi.org/10.1007/s10948-017-4420-y

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  • DOI: https://doi.org/10.1007/s10948-017-4420-y

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