The leaking soft stadium

Abstract

We soften the non zero y-boundary on a Bunimovich like quarter-stadium. The smoothing procedure is performed via an exponent monomial potential, the system becomes partially reflective, preserving the particle’s translation and rotational motion. By increasing the exponent value, the stadium’s boundaries become rigid and the system’s dynamics reaches a chaotic regime. We set a leaking soft stadium family by opening a limited region located at some place of its basis’s boundary, throughout which the particles can leak out. This work is an extension of our recently reported paper on this matter. We chase the particle’s trajectory and focus on the stadium transient behavior by means of the statistical analysis of the survival probability on the marginal orbits that never leave the system, the so called bouncing ball orbits. We compare these family orbits with the billiard’s transient chaos orbits.