Effective pair-interaction of phase singularities in random waves

TL;DR

This paper derives an effective pair-interaction model for phase singularities in 2D random waves, revealing liquid-like correlations and introducing a novel approach for analyzing topological defects in complex systems.

Contribution

It presents a new method to derive pair-interactions of phase singularities from their pair correlation function using reverse Monte Carlo, applicable to various systems.

Findings

Phase singularities exhibit liquid-like spatial correlations.

An effective pair-interaction potential is derived for these singularities.

The approach can be generalized to other topological defects.

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.