Parity-dependent localization in $N$ strongly coupled chains

TL;DR

This paper investigates how the localization of wave functions in disordered coupled chains depends on the number of chains and boundary conditions, revealing immunity effects and critical scaling behaviors.

Contribution

It uncovers parity-dependent localization phenomena and provides a perturbative explanation for the N-dependent localization strength in coupled disordered chains.

Findings

Weaker localization for small inter-chain coupling when N is odd or multiple of four.

Stronger localization when inter-chain coupling is much larger than longitudinal hopping.

Critical scaling of localization with the number of chains N.

Abstract

Anderson localization of wave-functions at zero energy in quasi-1D systems of $N$ disordered chains with inter-chain coupling $t$ is examined. Localization becomes weaker than for the 1D disordered chain ($t=0$) when $t$ is smaller than the longitudinal hopping $t'=1$, and localization becomes usually much stronger when $t\gg t'$. 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 four), with localization that is weaker than for $t=0$ and rather insensitive to $t$ when $t \gg t'$. The peculiar $N$-dependence and a critical scaling with $N$ is explained by a perturbative treatment in $t'/t$, 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.