Singular continuous spectra in a pseudo-integrable billiard

The pseudo-integrable barrier billiard invented by Hannay and McCraw [J. Phys. A 23, 887 (1990)] -- rectangular billiard with line-segment barrier placed on a symmetry axis -- is generalized. It is proven that the flow on invariant surfaces of genus two exhibits a singular continuous spectral component.Comment: 4 pages, 2 figure

The triangle map: a model of quantum chaos

We study an area preserving parabolic map which emerges from the Poincar\' e map of a billiard particle inside an elongated triangle. We provide numerical evidence that the motion is ergodic and mixing. Moreover, when considered on the cylinder, the motion appear to follow a gaussian diffusive process.Comment: 4 pages in RevTeX with 4 figures (in 6 eps-files

Accelerating cycle expansions by dynamical conjugacy

Periodic orbit theory provides two important functions---the dynamical zeta function and the spectral determinant for the calculation of dynamical averages in a nonlinear system. Their cycle expansions converge rapidly when the system is uniformly hyperbolic but greatly slowed down in the presence of non-hyperbolicity. We find that the slow convergence can be associated with singularities in the natural measure. A properly designed coordinate transformation may remove these singularities and results in a dynamically conjugate system where fast convergence is restored. The technique is successfully demonstrated on several examples of one-dimensional maps and some remaining challenges are discussed

Bifractality of the Devil's staircase appearing in the Burgers equation with Brownian initial velocity

It is shown that the inverse Lagrangian map for the solution of the Burgers equation (in the inviscid limit) with Brownian initial velocity presents a bifractality (phase transition) similar to that of the Devil's staircase for the standard triadic Cantor set. Both heuristic and rigorous derivations are given. It is explained why artifacts can easily mask this phenomenon in numerical simulations.Comment: 12 pages, LaTe

The Cleo Rich Detector

We describe the design, construction and performance of a Ring Imaging Cherenkov Detector (RICH) constructed to identify charged particles in the CLEO experiment. Cherenkov radiation occurs in LiF crystals, both planar and ones with a novel ``sawtooth''-shaped exit surface. Photons in the wavelength interval 135--165 nm are detected using multi-wire chambers filled with a mixture of methane gas and triethylamine vapor. Excellent pion/kaon separation is demonstrated.Comment: 75 pages, 57 figures, (updated July 26, 2005 to reflect reviewers comments), to be published in NIM

Constraints on B--->pi,K transition form factors from exclusive semileptonic D-meson decays

According to the heavy-quark flavour symmetry, the $B\to \pi, K$ transition form factors could be related to the corresponding ones of D-meson decays near the zero recoil point. With the recent precisely measured exclusive semileptonic decays $D \to \pi \ell \nu$ and $D\to K \ell \nu$, we perform a phenomenological study of $B \to \pi, K$ transition form factors based on this symmetry. Using BK, BZ and Series Expansion parameterizations of the form factor slope, we extrapolate $B \to \pi, K$ transition form factors from $q^{2}_{max}$ to $q^{2}=0$. It is found that, although being consistent with each other within error bars, the central values of our results for $B \to \pi, K$ form factors at $q^2=0$, $f_+^{B\to \pi, K}(0)$, are much smaller than predictions of the QCD light-cone sum rules, but are in good agreements with the ones extracted from hadronic B-meson decays within the SCET framework. Moreover, smaller form factors are also favored by the QCD factorization approach for hadronic B-meson decays.Comment: 19 pages, no figure, 5 table

A pseudointegrable Andreev billiard

A circular Andreev billiard in a uniform magnetic field is studied. It is demonstrated that the classical dynamics is pseudointegrable in the same sense as for rational polygonal billiards. The relation to a specific polygon, the asymmetric barrier billiard, is discussed. Numerical evidence is presented indicating that the Poincare map is typically weak mixing on the invariant sets. This link between these different classes of dynamical systems throws some light on the proximity effect in chaotic Andreev billiards.Comment: 5 pages, 5 figures, to appear in PR

Nonlinearity effects in the kicked oscillator

The quantum kicked oscillator is known to display a remarkable richness of dynamical behaviour, from ballistic spreading to dynamical localization. Here we investigate the effects of a Gross Pitaevskii nonlinearity on quantum motion, and provide evidence that the qualitative features depend strongly on the parameters of the system.Comment: 4 pages, 5 figure

Quantum localization and cantori in chaotic billiards

We study the quantum behaviour of the stadium billiard. We discuss how the interplay between quantum localization and the rich structure of the classical phase space influences the quantum dynamics. The analysis of this model leads to new insight in the understanding of quantum properties of classically chaotic systems.Comment: 4 pages in RevTex with 4 eps figures include