Escaping Dynamics in the Presence of Dissipation and Noise in Scattering Systems

Chaotic scattering in open Hamiltonian systems is a problem of fundamental interest with applications in several branches of physics. In this paper we analyze the effects of adding external perturbations such as dissipation and noise in chaotic scattering phenomena. Our main result is the exponential decay rate of the particles in the scattering region when the system is affected by dissipation and noise. In the case of dissipation the particles escape more slowly from the scattering region than in the conservative case. However, in the noisy case, the particles escape faster from the scattering region as compared to the noiseless case. Moreover, we analyze the fractal dimension of the set of singularities of the scattering function for the dissipative and the conservative cases. As a result of our analysis we have found that a scaling law exists between the exponential decay rate of the particles and the dissipative parameter, and that the fractal dimension for the noisy case is the unity.