Precise relation between branched-flow patterns and potential shape

Determine the precise relationship between observed branched-flow patterns and the shape of the weak refracting potential V(x,y) that generates them in the semiclassical forward-scattering regime, encompassing both smooth random Gaussian-correlated potentials and periodic potentials such as the Fermi lattice potential and sine-lattice potential, and quantify how specific potential features control branch formation and evolution.

Background

Branched flow arises when waves or rays propagate through weakly refracting media, producing arborescent concentration patterns. Most prior work has focused on smooth random potentials, even though branched flow has been recently confirmed in periodic media where superwires (indefinitely stable branches) may also occur.

The paper emphasizes that despite widespread observations across physical systems and advances in semiclassical understanding, a rigorous, predictive link between the form of the potential landscape and the resulting branched-flow structure has not been established. This gap motivates the paper of both random and periodic potentials to uncover general laws of branch birth and decay.