Properties of Two-Level Systems

  • W. A. Phillips
Part of the Physics of Solids and Liquids book series (PSLI)


The easiest way to introduce this subject is by showing some early results on the thermal properties of vitreous silica and other amorphous solids. The heat capacity(1) C and thermal conductivity(1) к are shown as functions of the absolute temperature T in Figures 14.1 and 14.2. Also shown in these figures are C and к for a similar crystalline material, α-quartz, which can be used to review the behavior expected on the basis of simple theories.


Heat Capacity Chalcogenide Glass Amorphous Solid Amorphous Metal Tunneling Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D. P. Jones, Thesis (1982) after R. C. Zeller and R. O. Pohl, Phys. Rev. B 4, 2029 (1971).CrossRefGoogle Scholar
  2. 2.
    R. B. Stephens, Phys. Rev. B 8, 2896 (1973).CrossRefGoogle Scholar
  3. 3.
    D. Redfield, Phys. Rev. Lett. 27, 730 (1971).CrossRefGoogle Scholar
  4. 4.
    P. Fulde and H. Wagner, Phys. Rev. Lett. 27, 1280 (1971).CrossRefGoogle Scholar
  5. 5.
    D. P. Jones, N. Thomas, and W. A. Phillips, Philos. Mag. B 38, 271 (1978).CrossRefGoogle Scholar
  6. 6.
    W. F. Love, Phys. Rev. Lett. 31, 822 (1973).CrossRefGoogle Scholar
  7. 7.
    W. A. Phillips, ed., Amorphous Solids: Low Temperature Properties, Springer-Verlag, Berlin (1981).Google Scholar
  8. 8.
    E. Merzbacher, Quantum Mechanics, 2nd edn., John Wiley and Sons, New York (1970).Google Scholar
  9. 9.
    M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York (1970).Google Scholar
  10. 10.
    J. Zimmermann and G. Weber, Phys. Rev. Lett. 46, 661 (1981).CrossRefGoogle Scholar
  11. 11.
    M. Meissner and K. Spitzmann, Phys. Rev. Lett. 46, 265 (1981).CrossRefGoogle Scholar
  12. 12.
    B. Golding, J. E. Graebner, and R. J. Shutz, Phys. Rev. B 14, 1660 (1976).CrossRefGoogle Scholar
  13. 13.
    L. Piché, R. Maynard, S. Hunklinger, and J. Jäckle, Phys. Rev. Lett. 32, 1426 (1974).CrossRefGoogle Scholar
  14. 14.
    S. Hunklinger and M. v Schickfus, J. Phys. C 9, L439 (1976).Google Scholar
  15. 15.
    B. Wright, Thesis, University of Cambridge (1982).Google Scholar
  16. 16.
    L. Bernard, Thèse, Grenoble (1979).Google Scholar
  17. 17.
    B. Golding, M. v Schickfus, S. Hunklinger, and K. Dransfield, Phys. Rev. Lett. 43, 1817 (1979).CrossRefGoogle Scholar
  18. 18.
    B. Golding and J. E. Graebner, in: Amorphous Solids: Low Temperature Properties ( W. A. Phillips, ed.), Springer-Verlag, Berlin (1981).Google Scholar
  19. 19.
    W. Arnold, C. Martinon, and S. Hunklinger, J. Phys. C 6, 961 (1978).Google Scholar
  20. 20.
    R. B. Stephens, Phys. Rev. B 13, 852 (1976).CrossRefGoogle Scholar
  21. 21.
    W. A. Phillips, Philos. Mag. B 43, 747 (1981).Google Scholar
  22. 22.
    J. C. Lasjaunias, A. Ravex, M. Vandorpe, and S. Hunklinger, Solid State Commun. 17, 1045 (1975).CrossRefGoogle Scholar
  23. 23.
    J. E. Graebner, B. Golding, R. J. Schutz, F. S. L. Hsu, and H. S. Chen, Phys. Rev. Lett. 39, 1480 (1977).CrossRefGoogle Scholar
  24. 24.
    H. v Lohneysen, Phys. Rep. 79, 161 (1981).CrossRefGoogle Scholar
  25. 25.
    P. Doussineau, P. Legros, A. Levelut, and A. Robin, J. Phys. (Paris) 39L, 265 (1978).CrossRefGoogle Scholar
  26. 26.
    W. Arnold, P. Doussineau, C. Frénois, and A. Levelut, J. Phys. (Paris) Lett. 42, L289 (1981).CrossRefGoogle Scholar
  27. 27.
    L. F. Lou, Solid State Commun. 19, 335 (1976).CrossRefGoogle Scholar
  28. 28.
    L. Anderson and H. E. Bommel, J. Am. Ceram. Soc. 38, 125 (1955).CrossRefGoogle Scholar
  29. 29.
    K. S. Gilroy and W. A. Phillips, J. Non-Cryst. Solids 35–36, 1135 (1980).CrossRefGoogle Scholar
  30. 30.
    H. v Lohneysen and H. J. Schink, Phys. Rev. Lett. 48, 1121 (1982).CrossRefGoogle Scholar
  31. 31.
    M. v Haumeder, U. Strom, and S. Hunklinger, Phys. Rev. Lett. 44, 84 (1980).CrossRefGoogle Scholar
  32. 32.
    M. R. Vukcevich, J. Non-Cryst. Solids 11, 25 (1972).CrossRefGoogle Scholar
  33. 33.
    K. K. Mon and N. W. Ashcroft, Solid State Commun 27, 609 (1978).CrossRefGoogle Scholar
  34. 34.
    D. A. Smith, Phys. Rev. Lett. 42, 729 (1979).CrossRefGoogle Scholar
  35. 35.
    R. A. Street and N. F. Mott, Phys. Rev. Lett. 35, 1293 (1975).CrossRefGoogle Scholar
  36. 36.
    P. W. Anderson, Phys. Rev. Lett. 34, 953 (1975).CrossRefGoogle Scholar
  37. 37.
    M. Kastner, J. Non-Cryst. Solids 31, 223 (1978).CrossRefGoogle Scholar
  38. 38.
    S. R. Elliott, Philos. Mag. 37, 553 (1978).CrossRefGoogle Scholar
  39. 39.
    D. L. Fox, B. Golding, and W. H. Haemmerle, Phys. Rev. Lett. 49, 1356 (1982).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • W. A. Phillips
    • 1
  1. 1.Cavendish Laboratory, Department of PhysicsUniversity of CambridgeCambridgeEngland

Personalised recommendations