Summary: Europhys. Lett., 60 (6), pp. 889895 (2002)
EUROPHYSICS LETTERS 15 December 2002
Coupling sensitivity of localization length
in one-dimensional disordered systems
R. Zillmer, V. Ahlers and A. Pikovsky
Department of Physics, University of Potsdam
Postfach 601553, D-14415 Potsdam, Germany
(received 13 August 2002; accepted 7 October 2002)
PACS. 72.15.Rn Localization effects (Anderson or weak localization).
Abstract. We investigate Anderson localization in a quasione-dimensional disordered
system consisting of weakly coupled statistically independent channels. The dependence of
the localization length on the coupling is shown to be singular: proportional to 1/| ln |.
Numerical evidence is given for coupled random chains with different statistics of site potential.
An analytical approach is developed based on the Fokker-Planck treatment of the coupled
stationary Schr¨odinger equations with Gaussian delta-correlated potentials.
Anderson localization, i.e. an exponential in average decay of the amplitude of the wave
function in space, is a fundamental phenomenon in disordered systems . It results from
a combination of tunneling and interference effects at the motion of a particle in a random
potential. In terms of condensed-matter physics, the disorder relates to impurities, vacancies
and dislocations in the crystal lattice. The exponential localization of the wave function plays