Brownian soliton motion

TL;DR

This paper uncovers fundamental analogies between soliton motion in random photonic lattices and Brownian motion, showing linear growth of displacement with distance and lattice depth, revealing new insights into soliton dynamics.

Contribution

It introduces the analogy between soliton dynamics in photonic lattices and Brownian motion, highlighting how soliton displacement behaves under different lattice conditions.

Findings

Average squared soliton displacement increases linearly with propagation distance.

Soliton displacement grows linearly with lattice depth in shallow lattices.

The dynamics exhibit a transition from ballistic to diffusive behavior.

Abstract

We reveal fundamental analogies between soliton dynamics in light-induced random photonic lattices and Brownian motion of particles. In particular, we discover that the average squared soliton displacement increases linearly with distance after an initial ballistic regime of propagation. We also find that in shallow lattices the average soliton displacement grows linearly with increasing lattice depth.