4,098 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
Chaotic Diffusion on Periodic Orbits: The Perturbed Arnol'd Cat Map
Chaotic diffusion on periodic orbits (POs) is studied for the perturbed
Arnol'd cat map on a cylinder, in a range of perturbation parameters
corresponding to an extended structural-stability regime of the system on the
torus. The diffusion coefficient is calculated using the following PO formulas:
(a) The curvature expansion of the Ruelle zeta function. (b) The average of the
PO winding-number squared, , weighted by a stability factor. (c) The
uniform (nonweighted) average of . The results from formulas (a) and (b)
agree very well with those obtained by standard methods, for all the
perturbation parameters considered. Formula (c) gives reasonably accurate
results for sufficiently small parameters corresponding also to cases of a
considerably nonuniform hyperbolicity. This is due to {\em uniformity sum
rules} satisfied by the PO Lyapunov eigenvalues at {\em fixed} . These sum
rules follow from general arguments and are supported by much numerical
evidence.Comment: 6 Tables, 2 Figures (postscript); To appear in Physical Review
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
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
Fractal Spectrum of a Quasi_periodically Driven Spin System
We numerically perform a spectral analysis of a quasi-periodically driven
spin 1/2 system, the spectrum of which is Singular Continuous. We compute
fractal dimensions of spectral measures and discuss their connections with the
time behaviour of various dynamical quantities, such as the moments of the
distribution of the wave packet. Our data suggest a close similarity between
the information dimension of the spectrum and the exponent ruling the algebraic
growth of the 'entropic width' of wavepackets.Comment: 17 pages, RevTex, 5 figs. available on request from
[email protected]
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
Dimer Decimation and Intricately Nested Localized-Ballistic Phases of Kicked Harper
Dimer decimation scheme is introduced in order to study the kicked quantum
systems exhibiting localization transition. The tight-binding representation of
the model is mapped to a vectorized dimer where an asymptotic dissociation of
the dimer is shown to correspond to the vanishing of the transmission
coefficient thru the system. The method unveils an intricate nesting of
extended and localized phases in two-dimensional parameter space. In addition
to computing transport characteristics with extremely high precision, the
renormalization tools also provide a new method to compute quasienergy
spectrum.Comment: There are five postscript figures. Only half of the figure (3) is
shown to reduce file size. However, missing part is the mirror image of the
part show
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
Peeping at chaos: Nondestructive monitoring of chaotic systems by measuring long-time escape rates
One or more small holes provide non-destructive windows to observe
corresponding closed systems, for example by measuring long time escape rates
of particles as a function of hole sizes and positions. To leading order the
escape rate of chaotic systems is proportional to the hole size and independent
of position. Here we give exact formulas for the subsequent terms, as sums of
correlation functions; these depend on hole size and position, hence yield
information on the closed system dynamics. Conversely, the theory can be
readily applied to experimental design, for example to control escape rates.Comment: Originally 4 pages and 2 eps figures incorporated into the text; v2
has more numerical results and discussion: now 6 pages, 4 figure
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