Random dimer model in pseudo two-dimensional lattices

TL;DR

This study investigates wave transport in pseudo-2D disordered lattices, revealing threshold behaviors, super-diffusive transport in correlated systems, and localization in uncorrelated or binary arrays, with implications for experimental realization.

Contribution

It demonstrates that 1D random dimer phenomena extend to pseudo-2D arrays, showing threshold effects and different transport regimes based on disorder correlations.

Findings

Threshold behavior depends on system size.

Super-diffusive transport occurs in short-range correlated lattices.

Localization is observed in uncorrelated and binary pseudo-2D arrays.

Abstract

In this work, we study long-time wave transport in correlated and uncorrelated disordered 2D arrays. When a separation of dimensions is applied to the model, we find that the predicted 1D random dimer phenomenology also appears in so-called pseudo-2D arrays. Therefore, a threshold behavior is observed in terms of the effective size for eigenmodes, as well as in long-time dynam- ics. For this threshold behavior to be observed a minimum system size is required, what is very important when considering a possible experimental realization. For the long-time evolution, we find that for short-range correlated lattices a super-diffusive long-range transport is observed, while for completely uncorrelated disorder in 2D transport becomes sub-diffusive within the localization length and random binary pseudo-2D arrays show localization.