Hyperbolic chaos in self-oscillating systems based on mechanical triple linkage: Testing absence of tangencies of stable and unstable manifolds for phase trajectories

Dynamical equations are formulated and a numerical study is provided for self-oscillatory model systems based on the triple linkage hinge mechanism of Thurston -- Weeks -- Hunt -- MacKay. We consider systems with holonomic mechanical constraint of three rotators as well as systems, where three rotators interact by potential forces. We present and discuss some quantitative characteristics of the chaotic regimes (Lyapunov exponents, power spectrum). Chaotic dynamics of the models we consider are associated with hyperbolic attractors, at least, at relatively small supercriticality of the self-oscillating modes; that follows from numerical analysis of the distribution for angles of intersection of stable and unstable manifolds of phase trajectories on the attractors. In systems based on rotators with interacting potential the hyperbolicity is violated starting from a certain level of excitation.Comment: 30 pages, 18 figure

Low Temperature Electronic Transport through Macromolecules and Characteristics of Intramolecular Electron Transfer

A theory of electronic transport through molecular wires is applied to analyze characteristics of a long-range electron transfer (ET) through molecular bridges in macromolecules with complex donor/acceptor subsystems. Assuming a coherent electron tunneling through the bridge to be the predominant mechanism of ET at low temperatures it is shown that low temperature current-voltage curves can exhibit a step-like structure, which contains information concerning intrinsic features of ET processes such as the effect of donor/acceptor coupling to the bridge and primary pathways of electrons tunneling through the bridge. By contacting the proposed theoretical analysis with such experimental data a variety of valuable characteristics of long-range intramolecular ET can be identified. Analytical and numerical results are presented. Using the Buttiker dephasing model within the scattering matrix formalism we analyze dephasing effects, and we show that these effects could be reduced enough to allow the structure of the electron transmission function to be exposed in the experiments on the electronic transport through macromolecules.Comment: 9 pages, 2 figures, text revise

K*-couplings for the antidecuplet excitation

We estimate the coupling of the K* vector meson to the N-->Theta+ transition employing unitary symmetry, vector meson dominance, and results from the GRAAL Collaboration for eta photoproduction off the neutron. Our small numerical value for the coupling constant is consistent with the non-observation of the Theta+ in recent CLAS searches for its photoproduction. We also estimate the K*-coupling for the N-->Sigma* excitation, with Sigma* being the Sigma-like antidecuplet partner of the Theta+-baryon.Comment: 9 pages, 1 figure. Minor changes in text and abstract, references added; version to appear in Phys. Rev.

Lyapunov exponents of quantum trajectories beyond continuous measurements

Quantum systems interacting with their environments can exhibit complex non-equilibrium states that are tempting to be interpreted as quantum analogs of chaotic attractors. Yet, despite many attempts, the toolbox for quantifying dissipative quantum chaos remains very limited. In particular, quantum generalizations of Lyapunov exponent, the main quantifier of classical chaos, are established only within the framework of continuous measurements. We propose an alternative generalization which is based on the unraveling of a quantum master equation into an ensemble of so-called 'quantum jump' trajectories. These trajectories are not only a theoretical tool but a part of the experimental reality in the case of quantum optics. We illustrate the idea by using a periodically modulated open quantum dimer and uncover the transition to quantum chaos matched by the period-doubling route in the classical limit.Comment: 5 pages, 4 figure

Behavior of radiation belts anomalous cosmic radionoise absorption in the aurora zone during the magnetic storms of 12-14 and 20-21 February 1964

Characteristics of radiation belt and ionospheric absorption of cosmic radio noise in auroral zone during geomagnetic storm

Formation of singularities on the surface of a liquid metal in a strong electric field

The nonlinear dynamics of the free surface of an ideal conducting liquid in a strong external electric field is studied. It is establish that the equations of motion for such a liquid can be solved in the approximation in which the surface deviates from a plane by small angles. This makes it possible to show that on an initially smooth surface for almost any initial conditions points with an infinite curvature corresponding to branch points of the root type can form in a finite time.Comment: 14 page