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arXiv · 1206.1922

Non-perturbative features of driven scattering systems

Andrea Cintio·Fulvio Cornolti
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Abstract

We investigate the scattering properties of one-dimensional, periodically and non-periodically forced oscillators. The pattern of singularities of the scattering function, in the periodic case, shows a characteristic hierarchical structure where the number Nc of zeros of the solutions plays the role of an order parameter marking the level of the observed self-similar structure. The behavior is understood both in terms of the return map and of the intersections pattern of the invariant manifolds of the outermost fixed points. In the non-periodic case the scattering function does not provide a complete development of the hierarchical structure. The singularities pattern of the outgoing energy as a function of the driver amplitude is connected to the arrangement of gaps in the fundamental regions. The survival probability distribution of temporarily bound orbits is shown to decay asymptotically as a power law. The "stickiness" of regular regions of phase space, given by KAM surfaces and remnant of KAM curves, is responsible for this observation.

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Andrea Cintio, Fulvio Cornolti. 2012-06-09. Non-perturbative features of driven scattering systems. https://arxiv.org/abs/1206.1922

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