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A quantum mechanical determination of the superfluid density

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Physik der kondensierten Materie

Abstract

The constituting conservation laws for a superfluid are quantum mechanically derived. Using thermodynamic relations the superfluid density is model-independently expressed in terms of reduced-density matrices. The general relation is illustrated for the Bogolubov model, and for two other approximations for the two-particle reduced-density matrix. The resulting relations between the densities of the super component and of the condensate are discussed.

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References

  1. For the work of the Bogolubov school.See: Z. M. Galasiewicz, Superconductivity and Quantum Fluids, Pergamon Press, Oxford 1970.

    Google Scholar 

  2. Hohenberg, P. C., Martin, P. C.: Ann. Phys. (N.Y.)34, 291 (1956).

    Article  Google Scholar 

  3. Kane, J. W., Kadanoff, L. P.: J. math. Phys.6, 1902 (1965).

    Article  Google Scholar 

  4. Weller, W.: Z. Naturforsch.A19, 410 (1964).

    Google Scholar 

  5. Usui, T.: Progr. theor. Phys.32, 190 (1964).

    Article  ADS  MathSciNet  Google Scholar 

  6. Halperin, B. I., Hohenberg, P. C.: Phys. Rev.188, 898 (1969).

    Article  ADS  Google Scholar 

  7. Gavoret, J., Nozières, P.: Ann. Phys. (N.Y.)28, 349 (1964).

    Article  Google Scholar 

  8. Haug, H., Weiss, K.: Lettere al Nuovo Cimento2, 887 (1971) and Physica.59, 29 (1972).

    Google Scholar 

  9. De Pasquale, F., Tabet, E.: Ann. Phys. (N.Y.)51, 223 (1969).

    Article  Google Scholar 

  10. Hyland, G. J., Rowlands, G.: Phys. Letters36 A, 233 (1971). J. Low Temp. Phys.7, No. 3/4 (1972). (In the letter an additional term in the entropy equation is erroneously missing).

    ADS  Google Scholar 

  11. Bogolubov, N.: J. Phys. USSR11, 23 (1947). Reprinted in D. Pines, The Many Body Problem, Benjamin, New York 1962.

    MathSciNet  Google Scholar 

  12. Fröhlich, H.: Phys. kondens. Materie9, 350 (1969).

    Google Scholar 

  13. Penrose, O., Onsager, L.: Phys. Rev.104, 576 (1956).

    Article  ADS  Google Scholar 

  14. Yang, C. N.: Rev. mod. Phys.34, 694 (1962).

    Article  ADS  Google Scholar 

  15. See e.g. Khalatnikov, I. M.: An Introduction to the Theory of Superfluidity, Benjamin, New York 1965.

    Google Scholar 

  16. Lal, P., Terreaux, Ch. M.: Preprint.

  17. Puff, R. D., Gillis, N. S.: Ann. Phys. (N.Y.)46, 364 (1968).

    Article  Google Scholar 

  18. Haug, H., Weiss, K.: Phys. Letters33 A, 263 (1970).

    ADS  Google Scholar 

  19. Putterman, S.: Private communication.

  20. Puff, R. D.: Phys. Rev. A,2, 1483 (1970).

    Article  ADS  Google Scholar 

  21. Haug, H., Weiss, K.: Phys. Rev. A,3, 717 (1971).

    Article  ADS  Google Scholar 

  22. Haug H., Weiss, K.: Phys. Letters39 A, 255 (1972).

    ADS  Google Scholar 

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Haug, H., Weiss, K. A quantum mechanical determination of the superfluid density. Phys kondens Materie 14, 324–335 (1972). https://doi.org/10.1007/BF02422689

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  • DOI: https://doi.org/10.1007/BF02422689

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