Diffusion on a one-dimensional lattice and quantum localization

Year: 1988

Authors: Schneider T., Politi A., Sörensen M.P.

Autors Affiliation: IBM Research Division, Zurich Research Laboratory, 8803 Rüschlikon, Switzerland;
Istituto Nazionale di Ottica, Largo E. fermi 6, 50125 Firenze, Italy;
Lab. of Applied Mathematics and Physics, The technical University of Denmark

Abstract: The problem of diffusion in modulated and random media as described by a master equation is reduced to a discrete Schrödinger equation, and further transformed into a recursive nonlinear map. Short- and long-time diffusion is then discussed in terms of dynamical properties of such a map. Analytical expressions for scaling behavior of the integrated density of states are derived for the top and bottom of the spectrum. The numerical results allow estimation of the scaling region and the corrections to the leading behavior.

Journal/Review: PHYSICAL REVIEW A

Volume: 37 (3)      Pages from: 948  to: 959

KeyWords: Schrödinger equation
DOI: 10.1103/PhysRevA.37.948

Citations: 4
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