2026/05/12 by Roberto Artuso, Matteo Burlo · 1 voice
Physics and Astronomy · #nlin.CD #math-ph
Billiards tables - a minimal model for particles moving in a confined region - are known to present classical (and quantum) different features according to their shape, ranging from strongly chaotic to integrable dynamics. Here we consider the role of a stochastic perturbation of the elastic reflection law, and show that while chaotic billiards maintain their key statistical feature, the behaviour for integrable billiard tables is completely different: it can be linked, for tiny perturbations, to Evans stochastic billiard, where at each collision the reflected angle is a uniformly distributed stochastic variable on (-π/2,π/2). The resulting spatial stationary measure has peculiar aspects, like being typically non uniform along the boundary, differently from any chaotic billiard table.