Advertisement

Momentum and Quasimomentum in the Physics of Condensed Matter

  • A. Thellung
Chapter

Abstract

In the first part of these lectures the formulations of hydrodynamics by Euler and by Lagrange are laid out. Eulerian phonons carry momenta, in contrast to Lagrangian phonons, whose momenta are zero, but the momentum density of the fluid is the same. The proof is much shorter than in earlier papers.

The second, main, part starts from the familiar concept of the quasimomen-tum of phonons and electrons in solids and proceeds to quasimomentum (in contrast to ordinary momentum) in the classical theory of elasticity and electrodynamics of continuous media. Conservation of quasimomentum is proven for arbitrarily nonlinear and anisotropic homogeneous media; it even holds for dispersive media, whose energy depends on higher than the first derivatives of the fields. If the difference between the local (Eulerian) coordinates (used in electrodynamics) and the material (Lagrangian) coordinates (used in the theory of elasticity) is properly taken into account a new term in the expression for the quasimomentum of photoelastic media appears. Various applications of quasimomentum conservation are mentioned and a new kind of radioelectric effect is put forward.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A. Thellung, Ann. Phys. 127, 289 (1980)ADSCrossRefGoogle Scholar
  2. A. Thellung. Thellung “Physics of Phonons”, edited by T. Paszkiewicz, Springer Lecture Notes in Physics, Vol. 285, 208 (1987)Google Scholar
  3. [2]
    H. Lamb, “Hydrodynamics”, Cambridge Univ. Press, London /New York, 1957Google Scholar
  4. [3]
    R. Kronig and A. Thellung, Physica 18, 749 (1952)MathSciNetADSzbMATHCrossRefGoogle Scholar
  5. [4]
    S.F. Tyabji, Proc. Cambr. Phil. Soc. 50, 449 (1954)MathSciNetADSzbMATHCrossRefGoogle Scholar
  6. [5]
    C. Kittel, “Quantum Theory of Solids”, Wiley, New York (1963)Google Scholar
  7. [6]
    A.A. Abrikosov, “Fundamentals of the Theory of Metals”, North- Holland, Amsterdam (1988)Google Scholar
  8. [7]
    L.D. Landau and E.M. Lifshitz, “Statistical Physics”, part one, Pergamon, Oxford (1980)Google Scholar
  9. [8]
    R. Peierls, in “Highlights of Condensed-Matter Theory”, ed. by F. Bassani, F. Fumi and M.P. Tosi, p. 237, North-Holland, Amsterdam (1985)Google Scholar
  10. [9]
    N.W. Ashcroft and N.D. Mermin, “Solid State Physics”, Holt, Rinehart and Winston, New York (1976)Google Scholar
  11. [10]
    L. D. Landau and E.M. Lifshitz, “Theory of Elasticity”, Pergamon, Oxford (1970)Google Scholar
  12. [11]
    V.L. Gurevich and A. Thellung, Phys. Rev. B 42, 7345 (1990)ADSCrossRefGoogle Scholar
  13. [12]
    I.M. Gilbert and B.R. Mollow, Am. J. Phys. 36, 822 (1968)ADSCrossRefGoogle Scholar
  14. [13]
    J.A. Kobussen, Helv. Phys. Acta 49, 599 (1976)Google Scholar
  15. [14]
    J.A. Kobussen and T. Paszkiewicz, Helv. Phys. Acta 54, 383 (1981)Google Scholar
  16. [15]
    N.N. Bogoliubov and D.V. Shirkov, “Introduction to the Theory of Quantized Fields”, Wiley, New York (1980)Google Scholar
  17. [16]
    J.A. Kobussen and T. Paszkiewicz, Helv. Phys. Acta 54, 395 (1981)Google Scholar
  18. [17]
    J. de Boer, in “Liquid Helium”, edited by G. Careri, Academic, New York (1963)Google Scholar
  19. [18]
    I.M. Khalatnikov, “Introduction to the Theory of Superfluidity”, Benjamin, New York (1965)Google Scholar
  20. [19]
    V.L. Gurevich, “Transport in Phonon Systems”, North-Holland, Amsterdam (1986)Google Scholar
  21. [20]
    J.D. Jackson, “Classical Electrodynamics”, Wiley, New York (1962)Google Scholar
  22. [21]
    L.D. Landau and E.M. Lifshitz, “Electrodynamics of Continuous Media”, Pergamon, Oxford (1960)zbMATHGoogle Scholar
  23. [22]
    V.L. Gurevich and A. Thellung, Physica A 188, 654 (1992)ADSCrossRefGoogle Scholar
  24. [23]
    R.E. Peierls, “Quantum Theory of Solids”, Clarendon, Oxford (1955)zbMATHGoogle Scholar
  25. [24]
    H. Schoeller and A. Thellung, Ann. Phys. 220, 18 (1992)MathSciNetADSzbMATHCrossRefGoogle Scholar
  26. [25]
    H. Minkowski, Nachr. Ges. Wiss Göttingen, 53 (1908), Math. Ann. 68, 473 (1910)Google Scholar
  27. [26]
    M. Abraham, Rend. Circolo Mat. Palermo 28, 1 (1909); 30, 33 (1910)zbMATHCrossRefGoogle Scholar
  28. [27]
    E.I. Blount, Bell Teleph. Lab. Tech. Memo. 38139–38139 (1971)Google Scholar
  29. [28]
    J.P. Gordon, Phys. Rev. A 8, 14 (1973)ADSGoogle Scholar
  30. [29]
    R. Peierls, Proc. Roy. Soc. A 347, 475 (1976)MathSciNetADSCrossRefGoogle Scholar
  31. [30]
    G. Weinreich, Phys. Rev. 107, 317 (1957)ADSCrossRefGoogle Scholar
  32. [31]
    Y.V. Gulyaev and A. G. Kozorezov, Sov. Phys. Solid State 18, 82 (1976)Google Scholar
  33. [32]
    A.D. Wieck, H. Sigg and K. Ploog, Phys. Rev. Lett. 64, 463 (1990)ADSCrossRefGoogle Scholar
  34. [33]
    V. L. Gurevich, R. Laiho and A.V. Lashkul, Phys. Rev. Lett. 69, 180 (1992)ADSCrossRefGoogle Scholar
  35. [34]
    M. Lax and D.F. Nelson, Phys. Rev. B 13, 1777 (1976)MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1994

Authors and Affiliations

  • A. Thellung
    • 1
  1. 1.Institut für Theoretische Physik der Universität ZürichZürichSwitzerland

Personalised recommendations