4,142 research outputs found
Fractal diffusion coefficient from dynamical zeta functions
Dynamical zeta functions provide a powerful method to analyze low dimensional
dynamical systems when the underlying symbolic dynamics is under control. On
the other hand even simple one dimensional maps can show an intricate structure
of the grammar rules that may lead to a non smooth dependence of global
observable on parameters changes. A paradigmatic example is the fractal
diffusion coefficient arising in a simple piecewise linear one dimensional map
of the real line. Using the Baladi-Ruelle generalization of the
Milnor-Thurnston kneading determinant we provide the exact dynamical zeta
function for such a map and compute the diffusion coefficient from its smallest
zero.Comment: 8 pages, 2 figure
Instability statistics and mixing rates
We claim that looking at probability distributions of \emph{finite time}
largest Lyapunov exponents, and more precisely studying their large deviation
properties, yields an extremely powerful technique to get quantitative
estimates of polynomial decay rates of time correlations and Poincar\'e
recurrences in the -quite delicate- case of dynamical systems with weak chaotic
properties.Comment: 5 pages, 5 figure
Periodic orbit quantization of the Sinai billiard in the small scatterer limit
We consider the semiclassical quantization of the Sinai billiard for disk
radii R small compared to the wave length 2 pi/k. Via the application of the
periodic orbit theory of diffraction we derive the semiclassical spectral
determinant. The limitations of the derived determinant are studied by
comparing it to the exact KKR determinant, which we generalize here for the A_1
subspace. With the help of the Ewald resummation method developed for the full
KKR determinant we transfer the complex diffractive determinant to a real form.
The real zeros of the determinant are the quantum eigenvalues in semiclassical
approximation. The essential parameter is the strength of the scatterer
c=J_0(kR)/Y_0(kR). Surprisingly, this can take any value between plus and minus
infinity within the range of validity of the diffractive approximation kR <<4.
We study the statistics exhibited by spectra for fixed values of c. It is
Poissonian for |c|=infinity, provided the disk is placed inside a rectangle
whose sides obeys some constraints. For c=0 we find a good agreement of the
level spacing distribution with GOE, whereas the form factor and two-point
correlation function are similar but exhibit larger deviations. By varying the
parameter c from 0 to infinity the level statistics interpolates smoothly
between these limiting cases.Comment: 17 pages LaTeX, 5 postscript figures, submitted to J. Phys. A: Math.
Ge
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 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
The Cleo III Ring Imaging Cherenkov Detector
The CLEO detector has been upgraded to include a state of the art particle
identification system, based on the Ring Imaging Cherenkov Detector (RICH)
technology, in order to take data at the upgraded CESR electron positron
collider. The expected performance is reviewed, as well as the preliminary
results from an engineering run during the first few months of operation of the
CLEO III detector.Comment: 5 pages, 2 Figures Talk given by M. Artuso at 8th Pisa Meeting on
Advanced Detectors, May 200
Delocalized and Resonant Quantum Transport in Nonlinear Generalizations of the Kicked Rotor Model
We analyze the effects of a nonlinear cubic perturbation on the delta-Kicked
Rotor. We consider two different models, in which the nonlinear term acts
either in the position or in the momentum representation. We numerically
investigate the modifications induced by the nonlinearity in the quantum
transport in both localized and resonant regimes and a comparison between the
results for the two models is presented. Analyzing the momentum distributions
and the increase of the mean square momentum, we find that the quantum
resonances asymptotically are very stable with respect to the nonlinear
perturbation of the rotor's phase evolution. For an intermittent time regime,
the nonlinearity even enhances the resonant quantum transport, leading to
superballistic motion.Comment: 8 pages, 10 figures; to appear in Phys. Rev.
Oseledets' Splitting of Standard-like Maps
For the class of differentiable maps of the plane and, in particular, for
standard-like maps (McMillan form), a simple relation is shown between the
directions of the local invariant manifolds of a generic point and its
contribution to the finite-time Lyapunov exponents (FTLE) of the associated
orbit. By computing also the point-wise curvature of the manifolds, we produce
a comparative study between local Lyapunov exponent, manifold's curvature and
splitting angle between stable/unstable manifolds. Interestingly, the analysis
of the Chirikov-Taylor standard map suggests that the positive contributions to
the FTLE average mostly come from points of the orbit where the structure of
the manifolds is locally hyperbolic: where the manifolds are flat and
transversal, the one-step exponent is predominantly positive and large; this
behaviour is intended in a purely statistical sense, since it exhibits large
deviations. Such phenomenon can be understood by analytic arguments which, as a
by-product, also suggest an explicit way to point-wise approximate the
splitting.Comment: 17 pages, 11 figure
On the duality between periodic orbit statistics and quantum level statistics
We discuss consequences of a recent observation that the sequence of periodic
orbits in a chaotic billiard behaves like a poissonian stochastic process on
small scales. This enables the semiclassical form factor to
agree with predictions of random matrix theories for other than infinitesimal
in the semiclassical limit.Comment: 8 pages LaTe
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