Stochastically perturbed billiards: Fingerprints of chaos and universality classes

Billiards tables-a minimal model for particles moving in a confined region-are known to present different classical (and quantum) 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 behavior for integrable billiard tables is completely different: It can be linked, for tiny perturbations, to the Evans stochastic billiard, where at each collision the reflected angle is a uniformly distributed stochastic variable on (-pi /2, pi/2). The resulting spatial stationary measure has peculiar aspects, like being typically nonuniform along the boundary, differently from any chaotic billiard table.