Chaotic dynamics creates and destroys branched flow

TL;DR

This paper investigates how chaotic dynamics influence the formation and decay of branched flow in periodic potentials, revealing universal patterns and unique decay behaviors linked to Hamiltonian chaos.

Contribution

It uncovers the universal laws of branch formation in non-integrable potentials and introduces the concept of superwires affecting branch decay in periodic systems.

Findings

Chaotic dynamics drive branch formation across various potentials.

Periodic potentials exhibit unique branch decay due to superwires.

The interplay between branched flow and phase space structures is fundamental.

Abstract

The phenomenon of branched flow, visualized as a chaotic arborescent pattern of propagating particles, waves, or rays, has been identified in disparate physical systems ranging from electrons to tsunamis, with periodic systems only recently being added to this list. Here, we explore the laws governing the evolution of the branches in periodic potentials. On one hand, we observe that branch formation follows a similar pattern in all non-integrable potentials, no matter whether the potentials are periodic or completely irregular. Chaotic dynamics ultimately drives the birth of the branches. On the other hand, our results reveal that for periodic potentials the decay of the branches exhibits new characteristics due to the presence of infinitely stable branches known as superwires. Again, the interplay between branched flow and superwires is deeply connected to Hamiltonian chaos. In this work, we explore the relationships between the laws of branched flow and the structures of phase space, providing extensive numerical and theoretical arguments to support our findings.