Abstract
In this article, the motion of a single quantum particle on a lattice with stochastically fluctuating site energies is investigated. The model is characterized by three parameters: the matrix elementJ for coherent energy transfer between nearest neighbours and the strength Δ and correlation time 1/γ of the fluctuations. Because of the simple structure of its Hamiltonian, expressions for stochastic moments such as the mean square displacement can be derived, which are valid for strong fluctuations, no matter how slow their decay, and for weak fluctuations, in the short correlation time limit. The basic idea of the method is to treat the deterministic part of the motion as perturbation acting on the stochastic part. While this method was previously used to obtain the diffusion constant for fluctuations represented by dichotomic Markov processes (DMPs), now the more realistic situation of Gaussian Markov processes is treated. The resulting diffusion constants are compared with those of dichotomic systems. Major differences appear for strong fluctuations and long correlation times. Contrary to the DMP case, the diffusion constant turns out to be a monotonously increasing function of the inverse correlation time γ (withJ, Δ fixed), for all values of γ. Anderson localization is observed at γ=0 but disappears as γ increases.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anderson, P.W.: J. Phys. Soc. Jpn.9, 888 (1954)
Kubo, R.: J. Phys. Soc. Jpn.17, 1100 (1962)
Haken, H., Stoobl, G.: Exact treatment of coherent and incoherent triplet exciton migration. In: The triplet state. Zahlan, A. (ed.), pp. 311–314. London: Cambridge University Press 1967
Haken, H., Reineker, P.: Z. Phys.249, 253 (1972)
Reineker, P., Haken, H.: Z. Phys.250, 300 (1972)
Schwarzer, E., Haken, H.: Phys. Lett.42 A, 317 (1972)
Haken, H., Strobl, G.: Z. Phys.262, 135 (1973)
Schwarzer, E., Haken, H.: Opt. Commun.9, 64 (1973)
Reineker, P.: Phys. Lett.42 A, 389 (1973)
Reineker, P.: Z. Phys.261, 187 (1973)
Reineker, P.: Z. Naturforsch.29 a, 282 (1974)
Haken, H., Schwarzer, E.: Chem. Phys. Lett.27, 41 (1974)
Ovchinnikov, A.A., Érikhman, N.S.: Sov. Phys. JETP40, 733 (1975)
Reineker, P., Kühne, R.: Z. Phys. B — Condensed Matter22, 193 (1975)
Kühne, R., Reineker, P.: Z. Phys. B — Condensed Matter22, 201 (1975)
Reineker, P.: Phys. Rev. B19, 1999 (1976)
Metiu, H., Kitahara, K., Silbey, R., Ross, J.: Chem. Phys. Lett.43, 189 (1976)
Schwarzer, E., Haken, H.: Phys. Status Solidi (b)84, 253 (1977)
Reineker, P.: Exciton dynamics in molecular crystals and aggregates. Stochastic Liouville equation approach: coupled coherent and incoherent motion, optical line shapes, magnetic resonance phenomena. In: Springer Tracts in Modern Physics. Vol. 94, pp. 111–226. Berlin, Heidelberg, New York: Springer 1982
Behn, U., Weller, W.: Phys. Status Solidi (b)99, 71 (1980)
Behn, U.: Phys. Status Solidi (b)100, 129 (1980);104, 203 (1981)
Paquet, D., Leroux Hugon, P.: Phys. Rev. Lett.49, 1023 (1982)
Sumi, H.: J. Chem. Phys.67, 2943 (1977)
Blumen, A., Silbey, R.: J. Chem. Phys.69, 3589 (1978)
Kitahara, K., Haus, J.W.: Z. Phys. B — Condensed Matter32, 419 (1979)
Rips, I.B., Čápek, V.: Phys. Status Solidi (b)100, 451 (1980)
Jackson, B., Silbey, R.: J. Chem. Phys.75, 3293 (1978)
Inaba, Y.: J. Phys. Soc. Jpn.50, 2473 (1981)
Inaba, Y.: PhD Thesis, University of Tokyo (1982)
Inaba, Y.: J. Phys. Soc. Jpn.52, 3144 (1983)
Inaba, Y.: J. Non Cryst. Solids59 & 60, 85 (1983)
Kassner, K., Reineker, P.: Z. Phys. B — Condensed Matter59, 357 (1985)
Kassner, K., Reineker, P.: Z. Phys. B — Condensed Matter60, 87 (1985)
Reineker, P., Kassner, K.: Coherence in the transport of a quantum particle. In: Lasers and Synergetics. Graham, R., Wunderlin, A. (eds.), p. 175. Berlin, Heidelberg, New York: Springer 1987
Lindenberg, K., West, B.J.: Phys. Rev. Lett.51, 1370 (1983)
Lindenberg, K., West, B.J.: Phys. Rev. A30, 568 (1984)
Reineker, P., Kenkre, V.M., Kühne, R.: Phys. Lett.84 A, 294 (1981)
Grover, M.K., Silbey, R.: J. Chem. Phys.54, 4843 (1971)
Silbey, R., Munn, R.W.: J. Chem. Phys.72, 2763 (1980)
Anderson, P.W.: Phys. Rev.109, 1492 (1958)
Haus, J.W., Kehr, K.W.: Phys. Rep.150, 263 (1987)
Kenkre, V.M.: Exciton dynamics in molecular crystals and aggregates. The master equation approach: coherence, energy transfer, annihilation and relaxation. In: Springer Tracts in Modern Physics. Vol. 94, pp. 1–109. Berlin, Heidelberg, New York: Springer 1982
Silbey, R.: Ann. Rev. Phys. Chem.27, 203 (1976)
Kagan, Yu., Maksimov, L.A.: Sov. Phys. JETP38, 307 (1974)
Bourret, R.C., Frisch, U., Pouquet, A.: Physica65, 303 (1973)
Jung, P.: private communication
Fox, R.F.: Phys. Rep.48, 179 (1978)
Abramowitz, M., Stegun, I.A.: Handbook of mathematical functions. New York: Dover 1972
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kassner, K. Quantum diffusion on a lattice with gaussian fluctuating site energies. Z. Physik B - Condensed Matter 70, 229–239 (1988). https://doi.org/10.1007/BF01318305
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01318305