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Register a new userA New Paradigm in Chaotic Ray Scattering
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We introduce a new paradigm of 2D (electromagnetic) ray-chaos, featuring both guided and scattered rays in a dielectric layer with exponentially tapered refraction index backed by an undulated conductive surface, and illustrate its relevant features. Numerical simulations of the corresponding full-wave solution indicate that the system complies with Berrys conjecture in the asymptotic short wavelength limit.
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We study the quantum and classical scattering of Hamiltonian systems whose chaotic saddle is described by binary or ternary horseshoes. We are interested in parameters of the system for which a stable island, associated with the inner fundamental periodic orbit of the system exists and is large, but chaos around this island is well developed. In this situation, in classical systems, decay from the interaction region is algebraic, while in quantum systems it is exponential due to tunneling. In both cases, the most surprising effect is a periodic response to an incoming wave packet. The period of this self-pulsing effect or scattering echoes coincides with the mean period, by which the scattering trajectories rotate around the stable orbit. This period of rotation is directly related to the development stage of the underlying horseshoe. Therefore the predicted echoes will provide experimental access to topological information. We numerically test these results in kicked one dimensional models and in open billiards.
Exact analytical expressions for the cross-section correlation functions of chaotic scattering sys- tems have hitherto been derived only under special conditions. The objective of the present article is to provide expressions that are applicable beyond these restrictions. The derivation is based on a statistical model of Breit-Wigner type for chaotic scattering amplitudes which has been shown to describe the exact analytical results for the scattering (S)-matrix correlation functions accurately. Our results are given in the energy and in the time representations and apply in the whole range from isolated to overlapping resonances. The S-matrix contributions to the cross-section correla- tions are obtained in terms of explicit irreducible and reducible correlation functions. Consequently, the model can be used for a detailed exploration of the key features of the cross-section correlations and the underlying physical mechanisms. In the region of isolated resonances, the cross-section correlations contain a dominant contribution from the self-correlation term. For narrow states the self-correlations originate predominantly from widely spaced states with exceptionally large partial width. In the asymptotic region of well-overlapping resonances, the cross-section autocorrelation functions are given in terms of the S-matrix autocorrelation functions. For inelastic correlations, in particular, the Ericson fluctuations rapidly dominate in that region. Agreement with known analytical and with experimental results is excellent.
We present here a new approach of the partial control method, which is a useful control technique applied to transient chaotic dynamics affected by a bounded noise. Usually we want to avoid the escape of these chaotic transients outside a certain region $Q$ of the phase space. For that purpose, there exists a control bound such that for controls smaller than this bound trajectories are kept in a special subset of $Q$ called the safe set. The aim of this new approach is to go further, and to compute for every point of $Q$ the minimal control bound that would keep it in $Q$. This defines a special function that we call the safety function, which can provide the necessary information to compute the safe set once we choose a particular value of the control bound. This offers a generalized method where previous known cases are included, and its use encompasses more diverse scenarios.
This paper analyzes the security of a recent cryptosystem based on the ergodicity property of chaotic maps. It is shown how to obtain the secret key using a chosen-ciphertext attack. Some other design weaknesses are also shown.
The noise-enhanced trapping is a surprising phenomenon that has already been studied in chaotic scattering problems where the noise affects the physical variables but not the parameters of the system. Following this research, in this work we provide strong numerical evidence to show that an additional mechanism that enhances the trapping arises when the noise influences the energy of the system. For this purpose, we have included a source of Gaussian white noise in the Henon-Heiles system, which is a paradigmatic example of open Hamiltonian system. For a particular value of the noise intensity, some trajectories decrease their energy due to the stochastic fluctuations. This drop in energy allows the particles to spend very long transients in the scattering region, increasing their average escape times. This result, together with the previously studied mechanisms, points out the generality of the noise-enhanced trapping in chaotic scattering problems.
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