Eulerian and Lagrangian Phonons

  • A. Thellung
Conference paper
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 79)

Abstract

Hydrodynamic motion can be described either in the formulation of Euler or of Lagrange. Quantization leads to phonons, which in Euler’s case carry a momentum \(\hbar {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{k}}\) (k = wave vector) and in Lagrange’s case have no momentum. In spite of this difference, physically observable effects must be the same since the two representations are equivalent. This conclusion is confirmed in an explicit comparison of the two cases for the microscopic derivation of the two-fluid equations in liquid He II.

Keywords

Helium Dinates Librium Verse 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H. Lamb: Hydrodynamics, Cambridge Univ. Press, London/ New York, 1957Google Scholar
  2. 2.
    R. Kronig, Physica 19, 535 (1953)CrossRefMATHADSGoogle Scholar
  3. 3.
    J. de Boer: In Liquid Helium, ed. by G. Careri, Academic Press, New York, 1963, p. 1Google Scholar
  4. 4.
    I.M. Khalatnikov: Introduction to the Theory of Superfluidity, Benjamin, New York, 1965Google Scholar
  5. 5.
    W. van Saarloos: Physics 108A, 557 (1981)Google Scholar
  6. 6.
    A. Thellung: In Physics of Phonons, ed. by T.Paszkiewicz, Springer Lecture Notes in Physics, Vol. 285 (1987) p. 208CrossRefGoogle Scholar
  7. 7.
    R. Kronig and A. Thellung: Physics 18, 749 (1952)MATHMathSciNetGoogle Scholar
  8. 8.
    A. Thellung: Annals of Physics 127, 289 (1980)CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1989

Authors and Affiliations

  • A. Thellung
    • 1
  1. 1.Institut für Theoretische PhysikUniversität ZürichZürichSwitzerland

Personalised recommendations