Effective pair-interaction of phase singularities in random waves

Abstract

In two-dimensional random waves, phase singularities are point-like dislocations with a behavior reminiscent of interacting particles. This -- qualitative -- consideration, stems from the spatial arrangement of these entities, which finds its hallmark in a pair correlation reminiscent of liquid-like system. Starting from their pair correlation function, we derive an effective pair-interaction for phase singularities in random waves by using a reverse Monte Carlo method. This study initiates a new approach for the treatment of singularities in random waves and can be generalized to topological defects in any system.