Abstract
Strong interactions with lattice vibrations can lead to profound modifications in the transport of quasiparticles such as electrons or excitons moving in solids. Recent approaches to the problem of the description of such transport have been based on discrete nonlinear quantum evolution equations. This is a brief review of some aspects of this recent activity. The first part of the article consists of a bird’s- eye-view presentation of several recent results for the nonlinear quantum dimer as well as for spatially extended systems, and of their applications to various experiments ranging from muon spin relaxation to fluorescence depolarization. The second part focuses attention on a particular kind of the interplay of nonlinearity and of randomness in such systems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
T. D. Holstein, Ann Phys. (NY) 8, 325, 343 (1959);
D. Emin, Adv. Phys. 24, 305 (1975)
R. J. Silbey, Ann. Rev. Phys. Chem. 22, 203 (1976)
C. B. Duke and L. B. Schein, Physics Today 33, no. 2, 42 (1980)
V. M. Kenkre and P. Reineker, Exciton Dynamics in Molecular Crystals and Aggregates, ed. G. Hohler (Springer-Verlag, Berlin, 1982)
A. S. Davydov, J. Theor. Biol. 38, 559 (1973); Usp. Fiz. Nauk. 138, 603 (1982) and references therein
A. C. Scott, F. Y. Chu, and D. W. McLaughlin, Proc. I.E.E.E. 61, 1443 (1973)
J. C. Eilbeck, P. S. Lomdahl and A. C. Scott, Physica D 16, 318 (1985)
J. M. Hyman, D. W. McLaughlin and A. C. Scott, Physica D 3, 28 (1981)
D. W. Brown, K. Lindenberg and B. J. West, Phys. Rev. B 37, 2946 (1988)
V. M. Kenkre and D. K. Campbell, Phys. Rev. B 34, 4959 (1986)
V. M. Kenkre and G. P. Tsironis, Phys. Rev. B 35, 1473 (1987)
V. M. Kenkre, G. P. Tsironis and D. K. Campbell, in Nonlinearity in Condensed Matter, ed. A. R. Bishop, D. K. Campbell, P. Kumar and S. E. Trullinger, (Springer-Verlag 1987)
G. P. Tsironis and V. M. Kenkre, Phys. Letters A 127, 209 (1988)
V.M.Kenkre and G.P.Tsironis, Chem. Phys., to be published, Dec. (1988)
L. Cruzeiro-Hansson, P. L. Christiansen and J. N. Elgin, Phys. Rev. B 37, 7896 (1988)
M. Ablowitz, SIAM, Review 19, 663 (1977);
M. J. Ablowitz and J. F. Ladik, J. Math. Phys. 17, 1011 (1976)
K. W. Kehr and Kazuo Kitahara, J. Phys. Soc. Japan, 56, 889, 4289 (1987);
K. W. Kehr and Kazuo Kitahara, to be published.
V. M. Kenkre and H. -L. Wu, University of New Mexico preprint
R. Zwanzig, in Lectures in Theoretical Physics vol.III, ed. W. Brittin, B. Downs and J. Down (Interscience 1961)
H. -L. Wu and V. M. Kenkre, Phys. Rev. B 39, xxxx(1989) to be published; see also Bul. Am. Phys. Soc. 33, K 22–5 (1988)
D. W. Brown, K. Lindenberg and B. J. West, Phys. Rev. B 37, 2946 (1988)
T. S. Rahman, R. S. Knox and V. M. Kenkre, Chem. Phys. (1978)
V. M. Kenkre and H. -L. Wu, Bui. Am. Phys. Soc. 33, no. K 22–6 (1988)
M. Toda, Theory of Nonlinear Lattices (Springer-Verlag, Berlin 1981)
V. M. Kenkre, H.-L. Wu, and I. Howard, Bul. Am. Phys. Soc. 33, K 22–4 (1988)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kenkre, V.M. (1989). Nonlinearity and Randomness in Quantum Transport. In: Bishop, A.R., Campbell, D.K., Pnevmatikos, S. (eds) Disorder and Nonlinearity. Springer Proceedings in Physics, vol 39. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-74893-6_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-74893-6_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-74895-0
Online ISBN: 978-3-642-74893-6
eBook Packages: Springer Book Archive