4,342 research outputs found
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 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 and , we perform a
phenomenological study of transition form factors based on this
symmetry. Using BK, BZ and Series Expansion parameterizations of the form
factor slope, we extrapolate transition form factors from
to . It is found that, although being consistent with
each other within error bars, the central values of our results for form factors at , , 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
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