Skip to main content
Log in

Dispersion relations of wave modes in helium II layers

  • Published:
Zeitschrift für Physik A Hadrons and nuclei

Abstract

Dispersion relations of (sound-like) wave modes, which can exist in a helium II layer of arbitrary width, are calculated numerically. The basis of our considerations is the complete system of the linearized Landau-Khalamikov equations, in which only the dissipative processes involved with η and ζ2 are taken into account. Apart from the linearization, no approximation or averaging is performed. The thermal expansion of helium II is taken into account. Symmetry properties of the velocities of flow, usually required, are dropped here. A hint is given as to how all the Khalatnikov coefficients may be measured by sound absorption experiments.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Khalatnikov, I. M.: Introduction to the theory of superfluidity. In: Frontiers in physics. New York: W. A. Benjamin 1965.

    Google Scholar 

  2. Atkins, K. R.: Phys. Rev.113, 962 (1959).

    Article  ADS  Google Scholar 

  3. Pollack, G. L., Pellam, J. R.: Phys. Rev.137, A1676 (1965).

    Article  ADS  Google Scholar 

  4. Shapiro, K. A., Rudnick, I.: Phys. Rev.137, A1383 (1965).

    Article  ADS  Google Scholar 

  5. Sanikidze, D. G., Adamenko, I. N., Kaganov, M. I.: Soviet Phys. JETP25, 383 (1967).

    ADS  Google Scholar 

  6. Meinhold-Heerlein, L.: Z. Physik213, 152 (1968).

    Article  ADS  Google Scholar 

  7. Wiechert, H.: Dissertation, Mainz (1969).

  8. Wiechert, H., Meinhold-Heerlein, L.: Phys. Letters29A, 41 (1969); — J. Low Temp. Phys.4, 273 (1971).

    Article  ADS  Google Scholar 

  9. Adamenko, I. N., Kaganov, M. I.: Soviet Phys. JETP26, 394 (1968).

    ADS  Google Scholar 

  10. Karchava, T. A., Sanikidze, D. G.: Soviet Phys. JETP28, 1009 (1969);31, 988 (1970).

    ADS  Google Scholar 

  11. Kaganov, M. I., Sanikidze, D. G., Tkeshelavshvili, O. G., Yampols'skii, V. A.: Soviet Phys. JETP32, 445 (1971).

    ADS  Google Scholar 

  12. Kerr, E. C., Taylor, R. D.: Ann. Phys.26, 292 (1964).

    Article  ADS  Google Scholar 

  13. Peshkov, V. P.: Soviet Phys. JETP11, 580 (1960).

    Google Scholar 

  14. Woods, A. D. B., Hollis-Hallett, A. C.: Can. J. Phys.41, 596 (1963).

    Article  ADS  Google Scholar 

  15. Chase, C. E.: Phys. Fluids1, 193 (1958).

    Article  ADS  Google Scholar 

  16. Whitney, W. M., Chase, C. E.: Phys. Rev.158, 200 (1967).

    Article  ADS  Google Scholar 

  17. Kramers, H. C., Wassher, J. D., Gorter, C. J.: Physica18, 329 (1952).

    Article  ADS  Google Scholar 

  18. Hill, R. W., Lounasmaa, O. V.: Phil. Mag.2, 143 (1957).

    Article  ADS  Google Scholar 

  19. Dransfeld, L., Newell, J. A., Wilks, J.: Proc. Roy. Soc. (London), Ser.A243, 500 (1958).

    Article  ADS  Google Scholar 

  20. Wehrum, R. P.: To be published.

  21. Collatz, L.: Funktionalanalysis und numerische Mathematik. Berlin-Heidelberg-New York: Springer 1968.

    MATH  Google Scholar 

  22. Ostrowski, A. M.: Solution of equations and systems of equations. New York-London: Academic Press 1960.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

The authors would like to thank Prof. G. U. Schubert and Dr. R. Loos for useful discussions.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wehrum, R.P., Meinhold-Heerlein, L. Dispersion relations of wave modes in helium II layers. Z. Physik 259, 117–134 (1973). https://doi.org/10.1007/BF01392842

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01392842

Navigation