LOFAR observations of fine spectral structure dynamics in type IIIb radio bursts

Solar radio emission features a large number of fine structures demonstrating great variability in frequency and time. We present spatially resolved spectral radio observations of type IIIb bursts in the $30-80$ MHz range made by the Low Frequency Array (LOFAR). The bursts show well-defined fine frequency structuring called "stria" bursts. The spatial characteristics of the stria sources are determined by the propagation effects of radio waves; their movement and expansion speeds are in the range of 0.1-0.6c. Analysis of the dynamic spectra reveals that both the spectral bandwidth and the frequency drift rate of the striae increase with an increase of their central frequency; the striae bandwidths are in the range of ~20-100 kHz and the striae drift rates vary from zero to ~0.3 MHz s^-1. The observed spectral characteristics of the stria bursts are consistent with the model involving modulation of the type III burst emission mechanism by small-amplitude fluctuations of the plasma density along the electron beam path. We estimate that the relative amplitude of the density fluctuations is of dn/n~10^-3, their characteristic length scale is less than 1000 km, and the characteristic propagation speed is in the range of 400-800 km/s. These parameters indicate that the observed fine spectral structures could be produced by propagating magnetohydrodynamic waves

Interaction of a vortex ring with the free surface of ideal fluid

The interaction of a small vortex ring with the free surface of a perfect fluid is considered. In the frame of the point ring approximation the asymptotic expression for the Fourier-components of radiated surface waves is obtained in the case when the vortex ring comes from infinity and has both horizontal and vertical components of the velocity. The non-conservative corrections to the equations of motion of the ring, due to Cherenkov radiation, are derived.Comment: LaTeX, 15 pages, 1 eps figur

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

New boundary conditions for integrable lattices

New boundary conditions for integrable nonlinear lattices of the XXX type, such as the Heisenberg chain and the Toda lattice are presented. These integrable extensions are formulated in terms of a generic XXX Heisenberg magnet interacting with two additional spins at each end of the chain. The construction uses the most general rank 1 ansatz for the 2x2 L-operator satisfying the reflection equation algebra with rational r-matrix. The associated quadratic algebra is shown to be the one of dynamical symmetry for the A1 and BC2 Calogero-Moser problems. Other physical realizations of our quadratic algebra are also considered.Comment: 22 pages, latex, no figure

Dynamical boundary conditions for integrable lattices

Some special solutions to the reflection equation are considered. These boundary matrices are defined on the common quantum space with the other operators in the chain. The relations with the Drinfeld twist are discussed.Comment: LaTeX, 12page

The Exact Electron Propagator in a Magnetic Field as the Sum over Landau Levels on a Basis of the Dirac Equation Exact Solutions

The exact propagator for an electron in a constant uniform magnetic field as the sum over Landau levels is obtained by the direct derivation by standard methods of quantum field theory from exact solutions of the Dirac equation in the magnetic field. The result can be useful for further development of the calculation technique of quantum processes in an external active medium, particularly in the conditions of moderately large field strengths when it is insufficient to take into account only the ground Landau level contribution.Comment: 9 pages, LaTeX; v2: 3 misprints corrected, a note and 1 reference added; to appear in Int. J. Mod. Phys.

Smooth and Non-Smooth Dependence of Lyapunov Vectors upon the Angle Variable on a Torus in the Context of Torus-Doubling Transitions in the Quasiperiodically Forced Henon Map

A transition from a smooth torus to a chaotic attractor in quasiperiodically forced dissipative systems may occur after a finite number of torus-doubling bifurcations. In this paper we investigate the underlying bifurcational mechanism which seems to be responsible for the termination of the torus-doubling cascades on the routes to chaos in invertible maps under external quasiperiodic forcing. We consider the structure of a vicinity of a smooth attracting invariant curve (torus) in the quasiperiodically forced Henon map and characterize it in terms of Lyapunov vectors, which determine directions of contraction for an element of phase space in a vicinity of the torus. When the dependence of the Lyapunov vectors upon the angle variable on the torus is smooth, regular torus-doubling bifurcation takes place. On the other hand, the onset of non-smooth dependence leads to a new phenomenon terminating the torus-doubling bifurcation line in the parameter space with the torus transforming directly into a strange nonchaotic attractor. We argue that the new phenomenon plays a key role in mechanisms of transition to chaos in quasiperiodically forced invertible dynamical systems.Comment: 24 pages, 9 figure

Zipf's Law in Gene Expression

Using data from gene expression databases on various organisms and tissues, including yeast, nematodes, human normal and cancer tissues, and embryonic stem cells, we found that the abundances of expressed genes exhibit a power-law distribution with an exponent close to -1, i.e., they obey Zipf's law. Furthermore, by simulations of a simple model with an intra-cellular reaction network, we found that Zipf's law of chemical abundance is a universal feature of cells where such a network optimizes the efficiency and faithfulness of self-reproduction. These findings provide novel insights into the nature of the organization of reaction dynamics in living cells.Comment: revtex, 11 pages, 3 figures, submitted to Phys. Rev. Let

Microscopic examination of hot spots giving rise to nonlinearity in superconducting resonators

We investigate the microscopic origins of nonlinear rf response in superconducting electromagnetic resonators. Strong nonlinearity appearing in the transmission spectra at high input powers manifests itself through the emergence of jumplike features near the resonant frequency that evolve toward lower quality factor with higher insertion loss as the rf input power is increased. We directly relate these characteristics to the dynamics of localized normal regions (hot spots) caused by microscopic features in the superconducting material making up the resonator. A clear observation of hot-spot formation inside a Nb thin film self-resonant structure is presented by employing the microwave laser scanning microscope, and a direct link between microscopic and macroscopic manifestations of nonlinearity is established.Comment: 5 pages, 4 figure