Complexity of two-dimensional quasimodes at the transition from weak scattering to Anderson localization

Quasimodes of an open finite-size two-dimensional (2D) random system are computed and systematically characterized in terms of their spatial extension eta, complexity factor q(2), and phase distribution for a collection of random systems ranging from weakly scattering to localized systems. A rapid change is seen in eta and q(2) at the crossover from localized to diffusive which corresponds to the emergence of 2D extended multipeaked quasimodes analogous to the necklace states recently observed in one dimension. These 2D quasimodes are interpreted in terms of coupled localized states.