Abstract
For a solid state model described by a band matrix with diagonal elements depending periodically on the siteindex we determine the eigenstates and their localization length. The periodicity of the diagonal elements gives rise to the appearance of a pronounced peak structure of the eigenstates with the same period. The same type of peak-structure is present in the quasi-energy states of some periodically driven quantum systems, and can be associated with a nearly conversed quasi-momentum quantum number. We investigate the influence of the periodic peak structure on the nearest neighbor level spacing distribution and find that the nearly conserved quasi-momentum modifies but does not destroy the level repulsion expected for a Gaussian orthogonal ensemble.
Similar content being viewed by others
References
Lee, P.A., Ramakrishnan, T.V.: Rev. Mod. Phys.57, 287 (1985)
Izrailev, F.M.: Phys. Rev. Lett.56, 541 (1986)
Casati, G., Guarneri, I., Shepelyansky, D.L.: IEEE J. Quantum Electron. QE24, 1420 (1988)
Fishman, S., Grempel, D.R., Prange, R.E.: Phys. Rev. Lett.49, 509 (1982)
Akulin, V.M., Dykhne, A.M.: Zh. Eksp. Teor. Fiz.73, 2098 (1977)
Graham, R., Shepelyansky, D.L. (to be published)
Shepelyansky, D.L.: Physica D28, 103 (1987)
Roman, E., Wiecko, C.: Z. Phys. B — Condensed Matter62, 163 (1986)
Lloyd, P.: J. Phys. C2, 1717 (1969);
Thouless, D.J.: J. Phys. C5, 77 (1972)
Deng, Z., Eberly, J.H.: Phys. Rev. Lett.53, 1810 (1984)
Fishman, S., Prange, R.E., Griniasty, M.: Phys. Rev. A39, 1628 (1989)
Haake, F.: Quantum aspects of chaotic systems. Berlin, Heidelberg, New York: Springer 1990
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Graham, R., Höhnerbach, M. & Shepelyansky, D.L. Localization and level statistics in a one-dimensional solid state model with periodically modulated potential. Z. Physik B - Condensed Matter 82, 347–350 (1991). https://doi.org/10.1007/BF01357177
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01357177