Chaotic dynamics creates and destroys branched flow

Branched flow, characterized by chaotic arborescent patterns of propagating particles, waves, or rays, has been observed in various physical systems, from electrons to tsunamis. Periodic systems have only recently been included in these studies. In this work, we investigate the laws governing branch evolution in periodic potentials. We find that branch formation follows a consistent pattern across all non-integrable potentials, whether periodic or irregular, with chaotic dynamics driving branch creation. However, in periodic potentials, the decay of branches shows unique features due to the presence of infinitely stable branches, termed superwires. The interaction between branched flow and superwires is intricately linked to Hamiltonian chaos. Furthermore, at small particle energies close to the height of the periodic potential, we find an interesting link to anomalous diffusion. Our study combines numerical simulations and theoretical analysis to explore the relationship between branched flow and the structures of phase space, offering new insights into this complex phenomenon.