Abstract
The contribution of the population fluctuations of two-level systems in glasses to the dynamic structure factor\(S(\vec k,t)\) is calculated using the concept of elastic dipoles. Describing the two-level systems by the tunneling model, with reasonable assumptions about the distribution of tunneling frequencies an essentially logarithmic decay in time of\(S(\vec k,t)\) is obtained.
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Anderson, P.W., Halperin, B.I., Varma, C.: Phil. Mag.25, 1 (1972)
Phillips, W.A.: J. Low Temp. Phys.7, 351 (1972)
Jäckle, J.: Z. Physik257, 212 (1972)
Jäckle, J., Piché, L., Arnold, W., Hunklinger, S.: J. Non-Cryst. Solids20, 365 (1976)
Black, J.L., Halperin, B.I.: Phys. Rev. B16, 2879 (1977)
For a review see: Hunklinger, S., Arnold, W. in Physical Acoustics (ed. by W.P. Mason and R.N. Thurston) Vol. 12, p. 155. New York: Academic Press 1976
Black, J.L.: private communication, cited as Nr. 39 in Ref. 5
von Schickfus, M., Hunklinger, S.: J. Phys. C9, L439 (1976)
Kröner, E.: Erg. angew. Math. 5 (ed. by L. Collatz and F. Lösch). Berlin: Springer 1958
Joffrin, J., Levelut, A.: J. de Physique36, 811 (1976)
Golding, B., Graebner, J.E.: Phys. Rev. Letters37, 852 (1976)
Golding, B., Hunklinger, S., von Schickfus, M.: private communication
For a short review see: Muggli, J.: Phys. kondens. Materie12, 237 (1971)
Landau, L.D., Lifschitz, E.M.: Lehrbuch der Theoretischen Physik, Bd. VII, Berlin: Akademie-Verlag 1966
Ref. 9, § 16
Ref. 14, Problem to § 8
Ref. 9, § 19
This assumption was made for the analogous case of the polarizability tensor in Theodorakopoulos, N., Jäckle, J.: Phys. Rev. B14, 2637 (1976)
Ref. 4, Equation (49)
See e.g.: Forster, D.: Hydrodynamic fluctuations, broken symmetry, and correlation functions, Reading (Mass.): Benjamin 1975 Jäckle, J.: Einführung in die Transporttheorie, Braunschweig; Vieweg 1978, to appear
This section is closely related to Ref. 4, Sect. 3
In Ref. 5 the parametersε, Δ of this work are denoted byΔ, Δ 0
We thank Dr. E. Nowotny for this suggestion
Abramowitz, M., Stegun, I.A. (Eds.): Handbook of Mathematical Functions. New York: Dover Publ. 1965
Goubau, W.M., Tait, R.A.: Phys. Rev. Letters34, 1220 (1975)
Leaderman, H.: Elastic and creep properties of filamentous materials and other high polymers, Washington, D.C.: Textile Foundation 1944
Kurkjian, C.R.: Phys. Chem. Glasses4, 128 (1963)
Wilson, E.B., Decius, J.C., Cross, P.C.: Molecular Vibrations, p. 46ff, New York: McGraw-Hill 1955
Halperin, B.I.: The Glass Transition and the Nature of the Glassy State (ed. by M. Goldstein and R. Simha), Annals of the New York Acad. of Sciences279, 173 (1976)
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Jäckle, J., Jüngst, K.L. Density fluctuations from elastic dipoles in glasses at low temperatures. Z Physik B 30, 243–253 (1978). https://doi.org/10.1007/BF01320029
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DOI: https://doi.org/10.1007/BF01320029