Year: 2014
Type: article
Abstract: Anderson localization of wave functions at zero energy in quasi-one-dimensional (1D) systems of $N$ disordered chains with interchain coupling $t$ is examined. Localization becomes weaker than for the 1D disordered chain ($t=0$) when $t$ is smaller than the longitudinal hopping ${t}^{\ensuremath{'}}=1$, and localization becomes usually much stronger when $t\ensuremath{\gg}{t}^{\ensuremath{'}}$. This is not so for all $N$. We find ``immunity'' to strong localization for open (periodic) lateral boundary conditions when $N$ is odd (a multiple of 4), with localization that is weaker than for $t=0$ and rather insensitive to $t$ when $t\ensuremath{\gg}{t}^{\ensuremath{'}}$. The peculiar $N$ dependence and a critical scaling with $N$ are explained by a perturbative treatment in ${t}^{\ensuremath{'}}/t$, and the correspondence to a weakly disordered effective chain is shown. Our results could be relevant for experimental studies of localization in photonic waveguide arrays.
Source: Physical Review B
Authors: Dietmar Weinmann, S. N. Evangelou
Language: Latvian
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2020428101