4,493 research outputs found
Recycling Parrondo games
We consider a deterministic realization of Parrondo games and use periodic
orbit theory to analyze their asymptotic behavior.Comment: 12 pages, 9 figure
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
Anomalous transport: a deterministic approach
We introduce a cycle-expansion (fully deterministic) technique to compute the
asymptotic behavior of arbitrary order transport moments. The theory is applied
to different kinds of one-dimensional intermittent maps, and Lorentz gas with
infinite horizon, confirming the typical appearance of phase transitions in the
transport spectrum.Comment: 4 pages, 4 figure
Superstable cycles for antiferromagnetic Q-state Potts and three-site interaction Ising models on recursive lattices
We consider the superstable cycles of the Q-state Potts (QSP) and the
three-site interaction antiferromagnetic Ising (TSAI) models on recursive
lattices. The rational mappings describing the models' statistical properties
are obtained via the recurrence relation technique. We provide analytical
solutions for the superstable cycles of the second order for both models. A
particular attention is devoted to the period three window. Here we present an
exact result for the third order superstable orbit for the QSP and a numerical
solution for the TSAI model. Additionally, we point out a non-trivial
connection between bifurcations and superstability: in some regions of
parameters a superstable cycle is not followed by a doubling bifurcation.
Furthermore, we use symbolic dynamics to understand the changes taking place at
points of superstability and to distinguish areas between two consecutive
superstable orbits.Comment: 12 pages, 5 figures. Updated version for publicatio
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
Performance of a C4F8O Gas Radiator Ring Imaging Cherenkov Detector Using Multi-anode Photomultiplier Tubes
We report on test results of a novel ring imaging Cherenkov (RICH) detection
system consisting of a 3 meter long gaseous C4F8O radiator, a focusing mirror,
and a photon detector array based on Hamamatsu multi-anode photomultiplier
tubes. This system was developed to identify charged particles in the momentum
range from 3-70 GeV/c for the BTeV experiment.Comment: 28 pages, 23 figures, submitted to Nuclear Instruments and Method
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
Instability statistics and mixing rates
We claim that looking at probability distributions of 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\ue9 recurrences in the-quite-delicate case of dynamical systems with weak chaotic properties
Efficient Diagonalization of Kicked Quantum Systems
We show that the time evolution operator of kicked quantum systems, although
a full matrix of size NxN, can be diagonalized with the help of a new method
based on a suitable combination of fast Fourier transform and Lanczos algorithm
in just N^2 ln(N) operations. It allows the diagonalization of matrizes of
sizes up to N\approx 10^6 going far beyond the possibilities of standard
diagonalization techniques which need O(N^3) operations. We have applied this
method to the kicked Harper model revealing its intricate spectral properties.Comment: Text reorganized; part on the kicked Harper model extended. 13 pages
RevTex, 1 figur
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
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