Effect of noise in open chaotic billiards

TL;DR

This paper studies how white-noise perturbations affect the decay of survival probability in open chaotic billiards, revealing five distinct decay regimes and their dependence on noise and system parameters.

Contribution

It introduces a comprehensive analysis of noise effects on survival probability decay regimes in open billiards, combining new calculations with recent Hamiltonian system results.

Findings

Identification of five decay regimes in survival probability

Scaling laws for decay parameters with noise intensity

Numerical validation using annular billiard simulations

Abstract

We investigate the effect of white-noise perturbations on chaotic trajectories in open billiards. We focus on the temporal decay of the survival probability for generic mixed-phase-space billiards. The survival probability has a total of five different decay regimes that prevail for different intermediate times. We combine new calculations and recent results on noise perturbed Hamiltonian systems to characterize the origin of these regimes, and to compute how the parameters scale with noise intensity and billiard openness. Numerical simulations in the annular billiard support and illustrate our results.