More ergodic billiards with an infinite cusp

In a previous paper (nlin.CD/0107041) the following class of billiards was studied: For $f: [0, +\infty) \longrightarrow (0, +\infty)$ convex, sufficiently smooth, and vanishing at infinity, let the billiard table be defined by $Q$, the planar domain delimited by the positive $x$-semiaxis, the positive $y$-semiaxis, and the graph of $f$. For a large class of $f$ we proved that the billiard map was hyperbolic. Furthermore we gave an example of a family of $f$ that makes this map ergodic. Here we extend the latter result to a much wider class of functions.Comment: 13 pages, 4 figure

Escape Orbits for Non-Compact Flat Billiards

It is proven that, under some conditions on $f$, the non-compact flat billiard $\Omega = \{ (x,y) \in \R_0^{+} \times \R_0^{+};\ 0\le y \le f(x) \}$ has no orbits going {\em directly} to $+\infty$. The relevance of such sufficient conditions is discussed.Comment: 9 pages, LaTeX, 3 postscript figures available at http://www.princeton.edu/~marco/papers/ . Minor changes since previously posted version. Submitted to 'Chaos

Entropy production in a mesoscopic chemical reaction system with oscillatory and excitable dynamics

Stochastic thermodynamics of chemical reaction systems has recently gained much attention. In the present paper, we consider such an issue for a system with both oscillatory and excitable dynamics, using catalytic oxidation of carbon monoxide on the surface of platinum crystal as an example. Starting from the chemical Langevin equations, we are able to calculate the stochastic entropy production P along a random trajectory in the concentration state space. Particular attention is paid to the dependence of the time averaged entropy productionP on the system sizeN in a parameter region close to the deterministic Hopf bifurcation.In the large system size (weak noise) limit, we find that P N^{\beta} with {\beta}=0 or 1 when the system is below or abovethe Hopf bifurcation, respectively. In the small system size (strong noise) limit, P always increases linearly with N regardless of the bifurcation parameter. More interestingly,P could even reach a maximum for some intermediate system size in a parameter region where the corresponding deterministic system shows steady state or small amplitude oscillation. The maximum value of P decreases as the system parameter approaches the so-called CANARD point where the maximum disappears.This phenomenon could be qualitativelyunderstood by partitioning the total entropy production into the contributions of spikes and of small amplitude oscillations.Comment: 13 pages, 6 figure

Nonlinear interaction of light with Bose-Einstein condensate: new methods to generate subpoissonian light

We consider $\Lambda$-type model of the Bose-Einstein condensate of sodium atoms interacting with the light. Coefficients of the Kerr-nonlinearity in the condensate can achieve large and negative values providing the possibility for effective control of group velocity and dispersion of the probe pulse. We find a regime when the observation of the "slow" and "fast" light propagating without absorption becomes achievable due to strong nonlinearity. An effective two-level quantum model of the system is derived and studied based on the su(2) polynomial deformation approach. We propose an efficient way for generation of subpoissonian fields in the Bose-Einstein condensate at time-scales much shorter than the characteristic decay time in the system. We show that the quantum properties of the probe pulse can be controlled in BEC by the classical coupling field.Comment: 13 pages, 6 figures, 1 tabl

Collisional Energy Loss of Fast Charged Particles in Relativistic Plasmas

Following an argument by Kirzhnits we rederive an exact expression for the energy loss of a fast charged particle in a relativistic plasma using the quantum field theoretical language. We compare this result to perturbative calculations of the collisional energy loss of an energetic electron or muon in an electron-positron plasma and of an energetic parton in the quark-gluon plasma.Comment: 9 pages, LATEX, 2 PostScript figure

Magnetic Force Exerted by the Aharonov-Bohm Line

The problem of the scattering of a charge by the Aharonov-Bohm (AB) flux line is reconsidered in terms of finite width beams. It is shown that despite the left-right symmetry in the AB scattering cross-section, the charge is scattered asymmetrically. The asymmetry (i.e. magnetic force) originates from almost forward scattering within the angular size of the incident wave. In the paraxial approximation, the real space solution to the scattering problem of a beam is found as well as the scattering S-matrix. The Boltzmann kinetics and the Landau quantization in a random AB array are considered.Comment: 5 pages, RevTeX. Discussions of paraxial approximation to the Aharonov-Bohm solution (Cornu spiral) and S-matrix, are extended. References are adde

Escape orbits and Ergodicity in Infinite Step Billiards

In a previous paper we defined a class of non-compact polygonal billiards, the infinite step billiards: to a given decreasing sequence of non-negative numbers $\{p_{n}$, there corresponds a table \Bi := \bigcup_{n\in\N} [n,n+1] \times [0,p_{n}]. In this article, first we generalize the main result of the previous paper to a wider class of examples. That is, a.s. there is a unique escape orbit which belongs to the alpha and omega-limit of every other trajectory. Then, following a recent work of Troubetzkoy, we prove that generically these systems are ergodic for almost all initial velocities, and the entropy with respect to a wide class of ergodic measures is zero.Comment: 27 pages, 8 figure

Characterization of a hollow core fibre-coupled near field terahertz probe

We describe the design and performance of a freely positionable THz near field probe based on a hollow core photonic crystal fibre-coupled photoconducting dipole antenna with an integrated sub-wavelength aperture. Experimental studies of the spatial resolution are compared with detailed finite element electromagnetic simulations and imaging artefacts that are a particular feature of this type of device are discussed. We illustrate the potential applications with descriptions of time domain near field studies of surface waves on a metamaterial and multimode propagation in a parallel plate waveguide