Particle transport in open polygonal billiards: A scattering map.

This article focuses on the analytical derivation of an exact scattering map for open polygonal billiards with opening angle \(\alpha = \pi/2\), considering both finite and infinite horizon cases. Using the Zemlyakov–Katok construction, the authors unfold the billiard into translation surfaces and classify trajectories via interval exchange transformations based on singular directions, resulting in a partition of the coordinate space into families of trajectories with distinct symbolic itineraries. The scattering map enables precise calculation of dwell times and provides an analytical expression for the average speed of sub-leading ballistic fronts—persistent propagating modes observed in the tails of the particle displacement distribution. Numerical simulations confirm that these ballistic fronts correspond to families of trajectories characterized by specific regions in the partition, revealing a symbolic hierarchy and geometric selection rules that govern particle transport in infinite polygonal channels.