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Luttinger theorem and imbalanced Fermi systems

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Abstract

The proof of the Luttinger theorem, which was originally given for a normal Fermi liquid with equal spin populations formally described by the exact many-body theory at zero temperature, is here extended to an approximate theory given in terms of a “conserving” approximation also with spin imbalanced populations. The need for this extended proof, whose underlying assumptions are here spelled out in detail, stems from the recent interest in superfluid trapped Fermi atoms with attractive inter-particle interaction, for which the difference between two spin populations can be made large enough that superfluidity is destroyed and the system remains normal even at zero temperature. In this context, we will demonstrate the validity of the Luttinger theorem separately for the two spin populations for any “Φ-derivable” approximation, and illustrate it in particular for the self-consistent t-matrix approximation.

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References

  1. A.A. Abrikosov, L.P. Gorkov, I.E. Dzyaloshinski, in Methods of Quantum Field Theory in Statistical Physics (Dover, New York, 1963), Chap. 4

  2. P. Nozières, Theory of Interacting Fermi Systems (Benjamin, New York, 1964)

  3. G. Rickayzen, in Green’s Functions and Condensed Matter (Academic Press, London, 1980), Chap. 6

  4. J.M. Luttinger, J.C. Ward, Phys. Rev. 118, 1417 (1960)

    Article  ADS  MathSciNet  Google Scholar 

  5. J.M. Luttinger, Phys. Rev. 119, 1153 (1960)

    Article  ADS  MathSciNet  Google Scholar 

  6. M. Oshikawa, Phys. Rev. Lett. 84, 3370 (2000)

    Article  ADS  Google Scholar 

  7. A. Praz, J. Feldman, H. Knörrer, E. Trubowitz, Europhys. Lett. 72, 49 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  8. G. Baym, L.P. Kadanoff, Phys. Rev. 124, 287 (1961)

    Article  ADS  MathSciNet  Google Scholar 

  9. G. Baym, Phys. Rev. 127, 1391 (1962)

    Article  ADS  MathSciNet  Google Scholar 

  10. J. Ortloff, M. Balzer, M. Potthoff, Eur. Phys. J. B 58, 37 (2007)

    Article  ADS  Google Scholar 

  11. M.W. Zwierlein, A. Schirotzek, C.H. Schunck, W. Ketterle, Science 311, 492 (2006)

    Article  ADS  Google Scholar 

  12. G.B. Partridge, W. Li, R.I. Kamar, Y. Liao, R.G. Hulet, Science 311, 503 (2006)

    Article  ADS  Google Scholar 

  13. A. Perali, P. Pieri, G.C. Strinati, C. Castellani, Phys. Rev. B 66, 024510 (2002)

    Article  ADS  Google Scholar 

  14. P. Nozières, S. Schmitt-Rink, J. Low Temp. Phys. 59, 195 (1985)

    Article  ADS  Google Scholar 

  15. X.-J. Liu, H. Hu, Europhys. Lett. 75, 364 (2006)

    Article  ADS  Google Scholar 

  16. M.M. Parish, F.M. Marchetti, A. Lamacraft, B.D. Simons, Nat. Phys. 3, 124 (2007)

    Article  Google Scholar 

  17. T. Kashimura, R. Watanabe, Y. Ohashi, J. Low Temp. Phys. 171, 355 (2013)

    Article  ADS  Google Scholar 

  18. A. Tartari, Ph.D. Thesis, University of Camerino, 2011

  19. M. Urban, P. Schuck, Phys. Rev. A 90, 023632 (2014)

    Article  ADS  Google Scholar 

  20. A. Perali, F. Palestini, P. Pieri, G.C. Strinati, J.T. Stewart, J.P. Gaebler, T.E. Drake, D.S. Jin, Phys. Rev. Lett. 106, 060402 (2011)

    Article  ADS  Google Scholar 

  21. T. Kashimura, R. Watanabe, Y. Ohashi, Phys. Rev. A 86, 043622 (2012)

    Article  ADS  Google Scholar 

  22. R. Haussmann, W. Rantner, S. Cerrito, W. Zwerger, Phys. Rev. A 75, 023610 (2007)

    Article  ADS  Google Scholar 

  23. A.L. Fetter, J.D. Walecka, in Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971), Chap. 7

  24. G.C. Strinati, in The BCS-BEC Crossover and the Unitary Fermi Gas, edited by W. Zwerger, Lecture Notes in Physics (Springer-Verlag, Berlin, Heidelberg, 2012), Vol. 836, pp. 99–125

  25. R. Combescot, S. Giraud, Phys. Rev. Lett. 101, 050404 (2008)

    Article  ADS  Google Scholar 

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Correspondence to Giancarlo Calvanese Strinati.

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Pieri, P., Strinati, G.C. Luttinger theorem and imbalanced Fermi systems. Eur. Phys. J. B 90, 68 (2017). https://doi.org/10.1140/epjb/e2017-80071-2

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  • DOI: https://doi.org/10.1140/epjb/e2017-80071-2

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