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.
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References
Khalatnikov, I. M.: Introduction to the theory of superfluidity. In: Frontiers in physics. New York: W. A. Benjamin 1965.
Atkins, K. R.: Phys. Rev.113, 962 (1959).
Pollack, G. L., Pellam, J. R.: Phys. Rev.137, A1676 (1965).
Shapiro, K. A., Rudnick, I.: Phys. Rev.137, A1383 (1965).
Sanikidze, D. G., Adamenko, I. N., Kaganov, M. I.: Soviet Phys. JETP25, 383 (1967).
Meinhold-Heerlein, L.: Z. Physik213, 152 (1968).
Wiechert, H.: Dissertation, Mainz (1969).
Wiechert, H., Meinhold-Heerlein, L.: Phys. Letters29A, 41 (1969); — J. Low Temp. Phys.4, 273 (1971).
Adamenko, I. N., Kaganov, M. I.: Soviet Phys. JETP26, 394 (1968).
Karchava, T. A., Sanikidze, D. G.: Soviet Phys. JETP28, 1009 (1969);31, 988 (1970).
Kaganov, M. I., Sanikidze, D. G., Tkeshelavshvili, O. G., Yampols'skii, V. A.: Soviet Phys. JETP32, 445 (1971).
Kerr, E. C., Taylor, R. D.: Ann. Phys.26, 292 (1964).
Peshkov, V. P.: Soviet Phys. JETP11, 580 (1960).
Woods, A. D. B., Hollis-Hallett, A. C.: Can. J. Phys.41, 596 (1963).
Chase, C. E.: Phys. Fluids1, 193 (1958).
Whitney, W. M., Chase, C. E.: Phys. Rev.158, 200 (1967).
Kramers, H. C., Wassher, J. D., Gorter, C. J.: Physica18, 329 (1952).
Hill, R. W., Lounasmaa, O. V.: Phil. Mag.2, 143 (1957).
Dransfeld, L., Newell, J. A., Wilks, J.: Proc. Roy. Soc. (London), Ser.A243, 500 (1958).
Wehrum, R. P.: To be published.
Collatz, L.: Funktionalanalysis und numerische Mathematik. Berlin-Heidelberg-New York: Springer 1968.
Ostrowski, A. M.: Solution of equations and systems of equations. New York-London: Academic Press 1960.
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The authors would like to thank Prof. G. U. Schubert and Dr. R. Loos for useful discussions.
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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
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DOI: https://doi.org/10.1007/BF01392842