Abstract
A mode-coupling theory (MCT) is presented for the spin-boson model with a spectral density which accounts for a heat bath made up of lattice vibrations of a dielectric solid (superohmic dissipation). A usual decoupling approximation provides a set of non-linear integral equations which are solved both numerically by iteration on a computer and analytically by means of a frequency dependent ansatz for the memory functions. There is a transition to incoherent motion at a temperatureT * where the bare two-level energy is equal to the damping rate, in contradiction to results obtained previously from a path integral formulation. The discrepancy arises since in the MCT the relevant self-energy function does not exhibit a 1/z-pole atz=0. For tunnelling systems in dielectrics this yields a new relaxation mechanism due to incoherent tunnelling: the present results might require to modify some of the basic assumptions of the standard tunnelling model for dielectric glasses.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Caldeira, A.O., Leggett, A.J.: Ann. Phys. (N.Y.)149, 374 (1983);153, 445 (1983); Phys. Rev. Lett.46, 211 (1981)
Dorsey, A.T., Fisher, M.P.A., Wartak, M.S.: Phys. Rev. A33, 1117 (1986)
Leggett, A.J., Chakravarty, S., Dorsey, A.T., Fisher, M.P.A., Garg, A., Zwerger, W.: Rev. Mod. Phys.59, 1 (1987)
Weiss, U.: Quantum dissipative dynamics. Series in Modern Condensed Matter Physics, Vol. 2. Singapore: World Scientific 1993
Görlich, R., Weiss, U.: Phys. Rev. B38, 5254 (1988)
Weiss, U., Grabert, H., Linkwitz, S.: J. Low. Temp. Phys.68, 213 (1987)
Weiss, U., Grabert, H., Hänggi, P., Riseborough, P.: Phys. Rev. B35, 9535 (1987)
Weiss, U., Wollensack, M.: Phys. Rev. Lett.62, 1663 (1989)
Görlich, R., Sassetti, M., Weiss, U.: Europhys. Lett.10, 507 (1989)
Zwerger, W.: Z. Phys. B53, (1983); ibid54, 87 (1983)
Grabert, H., Dattagupta, S., Jung, R.: J. Phys. C1, 1405 (1989)
Egger, R., Weiss, U.: Z. Phys. B89, 97 (1992)
Beck, R., Götze, W., Preloysek, P.: Phys. Rev. A20, 1140 (1979)
Götze, W., Vujicic, G.M.: Phys. Rev. B38, 9398 (1988)
DeRaedt, B., DeRaedt, H.: Phys. Rev. B29, 5325 (1984)
Bray, A.J., Moore, N.A.: Phys. Rev. Lett.49, 1545 (1982)
Chakravarty, S.: Phys. Rev. Lett.49, 681 (1982)
Mori, H.: Progr. Theor. Phys.33, 127 (1965); Zwanzig, R.: J. Chem. Phys.33, 1338 (1960)
Forster, D.: Hydrodynamic fluctuations, broken symmetry and correlation functions. Reading, Mass: Benjamin Cummings 1975; Fick, E., Sauermann, G.: Quantenstatistik dynamischer Prozesse, Bd. IIa. Frankfurt: Deutsch 1986
Kawasaki, K.: Phys. Rev.150, 291 (1960)
Götze, W.: In: Les Houches 1989: Liquids, freezings and the glass transition
Würger, A.: Z. Phys. B85, 93 (1991)
Götze, W., Sjögren, L.: J. Phys. C17, 5759 (1984)
Grossmann, S.: Phys. Rev. A17, 1123 (1978)
Würger, A.: Z. Phys. B94, 173 (1994)
Piché, L., Maynard, R., Hunklinger, S., Jäckle, J.: Phys. Rev. Lett.32, 1426 (1974)
Jäckle, J., Piché, L., Arnold, W., Hunklinger, S.: J. Non-Cryst. Solids20, 365 (1976)
Hunklinger, S., Arnold, W.. In: Physical acoustics, vol. 12. Thurston, R.N., Mason W.P. (eds.) New York: Academic Press 1976
Hunklinger, S., Raychaudhuri, A.K.: In: Progress in low temperature physics, vol. IX. Brewer, D.F. (ed.) Amsterdam: Elsevier 1986
Anderson, P.W., Halperin, B.I., Varma, C.: Philos. Mag.25, 1 (1972)
Philips, W.A.: J. Low. Temp. Phys.7, 351 (1972)
Jäckle, J.: Z. Phys.257, 212 (1972)