Breaking parameter modulated chaotic secure communication system

This paper describes the security weakness of a recently proposed secure communication method based on parameter modulation of a chaotic system and adaptive observer-based synchronization scheme. We show that the security is compromised even without precise knowledge of the chaotic system used.Comment: 8 pages, 3 figures, latex forma

Exact Eigenfunctions of a Chaotic System

The interest in the properties of quantum systems, whose classical dynamics are chaotic, derives from their abundance in nature. The spectrum of such systems can be related, in the semiclassical approximation (SCA), to the unstable classical periodic orbits, through Gutzwiller's trace formula. The class of systems studied in this work, tiling billiards on the pseudo-sphere, is special in this correspondence being exact, via Selberg's trace formula. In this work, an exact expression for Green's function (GF) and the eigenfunctions (EF) of tiling billiards on the pseudo-sphere, whose classical dynamics are chaotic, is derived. GF is shown to be equal to the quotient of two infinite sums over periodic orbits, where the denominator is the spectral determinant. Such a result is known to be true for typical chaotic systems, in the leading SCA. From the exact expression for GF, individual EF can be identified. In order to obtain a SCA by finite series for the infinite sums encountered, resummation by analytic continuation in $\hbar$ was performed. The result is similar to known results for EF of typical chaotic systems. The lowest EF of the Hamiltonian were calculated with the help of the resulting formulae, and compared with exact numerical results. A search for scars with the help of analytical and numerical methods failed to find evidence for their existence.Comment: 53 pages LaTeX, 10 Postscript figure

Entanglement and teleportation via chaotic system

The dynamics of entangled state interacting with a single cavity mode is investigated in the presence of a random parameter. We have shown that degree of entanglement decays with time and rate of decay is defined by features of random parameter. Quantum teleportation through dissipative channal and teleportation fidelity as a function of damping rates has been studied. The sensitivity of the fidelity with respect to random parameter is discussed. We have evaluated the time interval during which one can perform the quantum teleportation and send the information with reasonable fidelity, for a given values of correlation length of random parameter.Comment: Accepted in Physica

A piece-wise affine contracting map with positive entropy

We construct the simplest chaotic system with a two-point attractor.Comment: 2 page

Quantum Dissipation and Decoherence via Interaction with Low-Dimensional Chaos: a Feynman-Vernon Approach

We study the effects of dissipation and decoherence induced on a harmonic oscillator by the coupling to a chaotic system with two degrees of freedom. Using the Feynman-Vernon approach and treating the chaotic system semiclassically we show that the effects of the low dimensional chaotic environment are in many ways similar to those produced by thermal baths. The classical correlation and response functions play important roles in both classical and quantum formulations. Our results are qualitatively similar to the high temperature regime of the Caldeira-Leggett model.Comment: 31 pages, 4 figure