Crossover From Branched Flow to Anderson Localization in Time-Fluctuating Random Potentials

Abstract

When a wavepacket propagates in a disordered system, two distinct phenomena, Anderson localization and branched flow, are known to occur. Anderson localization happens when the wavepacket becomes confined in a stationary random potential as it evolves, while branched flow occurs as the random potential fluctuates smoothly and slowly along the evolving dimension. In this study, the transition from branched flow to Anderson localization is investigated by progressively increasing the temporal correlation length of the random potential (denoted by $\tau$) in the evolving dimension. The wave dynamics is found initially showing hyper-diffusion due to enhanced branched flow, but with a further increase in $\tau$, a coherence-driven localization effect is triggered. This effect reduces diffusion and ultimately leads to Anderson localization. Two critical temporal correlation lengths $\tau$ are identified, at which the maximum diffusion rate is achieved, and at which Anderson localization dominates the wave evolution, respectively. A theoretical model is proposed that takes into account the interaction between wave coherence and the wave diffusion rate to predict these two critical correlation lengths $\tau$. The experimental observation of the transition from branched flow to Anderson localization with varying $\tau$ is demonstrated in the light propagation in photorefractive SBN:61 with a random potential introduced in a controlled manner.