Papers › Probabilistic description of dissipative chaotic scattering
Probabilistic description of dissipative chaotic scattering
Lachlan Burton, Holger Dullin, Eduardo G. Altmann
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We investigate the extent to which the probabilistic properties of a chaotic scattering system with dissipation can be understood from the properties of the dissipation-free system. For large energies E, a fully chaotic scattering leads to an exponential decay of the survival probability P(t) ∼e^(-κt) with an escape rate κ that decreases with E. Dissipation γ>0 leads to the appearance of different finite-time regimes in P(t). We show how these different regimes can be understood for small γ≪1 and t≫1/κ₀ from the effective escape rate κᵧ(t)=κ₀(E(t)) (including the non-hyperbolic regime) until the energy reaches a critical value E_c at which no escape is possible. More generally, we argue that for small dissipation γ and long times t the surviving trajectories in the dissipative system are distributed according to the conditionally invariant measure of the conservative system at the corresponding energy E(t)<E(0). Quantitative predictions of our general theory are compared with numerical simulations in the Henon-Heiles model.
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