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A variational approach to superfluidity

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Abstract

A variational approach to problems in quantum statistical mechanics is described and it is shown how to determine the best quasi-free approximation to the equilibrium state. The relation between this approximation and the Bogoliubov approximation in superfluidity is discussed.

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References

  1. J. G. Valatin and D. Butler,Nuovo Cimento 10:37 (1958).

    Google Scholar 

  2. M. Girardeau and R. Arnowitt,Phys. Rev. 113:755 (1959).

    Google Scholar 

  3. D.W. Robinson, inCargese Lectures in Physics, Vol. 4, D. Kastler, ed., Gordon and Breach, New York (1970); also inThe Thermodynamic Pressure in Quantum Statistical Mechanics, Vol. 9 ofLecture Notes in Physics, Springer Verlag, Berlin, Heidelberg, New York (1971).

    Google Scholar 

  4. D. Ruelle, inStatistical Mechanics and Quantum Field Theory, Les Houches 1970, C. De Witt and R. Stora, eds., Gordon and Breach, New York (1971).

    Google Scholar 

  5. A. S. Švarc,Trans. Mosc. Math. Soc. 22 (1970) [A.M.S. translation (1972)].

  6. D. W. Robinson,Commun. Math. Phys. 1:159 (1965).

    Google Scholar 

  7. N. N. Bogoliubov,J. Phys. (USSR)11:23 (1947); reprinted in D. Pines,The Many Body Problem, Benjamin, New York (1961).

    Google Scholar 

  8. M. Fannes and A. Verbeure,Ann. Soc. Sci. Brux. 87:87 (1973).

    Google Scholar 

  9. I. E. Segal,Can. J. Math. 13:1 (1961).

    Google Scholar 

  10. J. Slawny,Commun. Math. Phys. 24:151 (1972).

    Google Scholar 

  11. D. W. Robinson,Commun. Math. Phys. 1:89 (1965).

    Google Scholar 

  12. H. Araki,J. Math. Phys. 1:492 (1960).

    Google Scholar 

  13. J. T. Cannon,Commun. Math. Phys. 29:89 (1973).

    Google Scholar 

  14. G. F. Dell'Antonio, S. Doplicher, and D. Ruelle,Commun. Math. Phys. 2:223 (1966).

    Google Scholar 

  15. J. T. Lewis and J. V. Pulè,Commun. Math. Phys. 36:1 (1974).

    Google Scholar 

  16. E. B. Davies,Commun. Math. Phys. 28:69 (1972).

    Google Scholar 

  17. R. H. Critchley and J. T. Lewis, The Entropy Density of Quasi-Free States (in preparation).

  18. R. H. Critchley, D. Phil. Thesis, Oxford (1974).

  19. J. Ginibre,Commun. Math. Phys. 8:26 (1968).

    Google Scholar 

  20. A. I. Solomon,J. Math. Phys. 12:390 (1971).

    Google Scholar 

  21. H. Araki and E. J. Woods,J. Math. Phys. 4:637 (1963).

    Google Scholar 

  22. E. W. Packel,Functional Analysis, Intertext, New York (1974), p. 128.

    Google Scholar 

  23. R. H. Critchley, A Quasi-Free Approximation to the Equilibrium State of a Boson Gas (in preparation).

Download references

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Critchley, R.H., Solomon, A.I. A variational approach to superfluidity. J Stat Phys 14, 381–393 (1976). https://doi.org/10.1007/BF01030201

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