Parity-dependent localization in $N$ strongly coupled chains

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 $t^{\prime }=1$, and localization becomes usually much stronger when $t\gg t^{\prime }$. 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 $t\gg t^{\prime }$. The peculiar $N$-dependence and a critical scaling with $N$ is explained by a perturbative treatment in $t^{\prime }/t$, 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.

9 pages, 5 figures

References in corpus (2)

• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Anderson localization of one-dimensional hybrid particles