54 research outputs found
Parking and the visual perception of space
Using measured data we demonstrate that there is an amazing correspondence
among the statistical properties of spacings between parked cars and the
distances between birds perching on a power line. We show that this observation
is easily explained by the fact that birds and human use the same mechanism of
distance estimation. We give a simple mathematical model of this phenomenon and
prove its validity using measured data
Spectral statistics of chaotic systems with a point-like scatterer
The statistical properties of a Hamiltonian perturbed by a localized
scatterer are considered. We prove that when describes a bounded chaotic
motion, the universal part of the spectral statistics are not changed by the
perturbation. This is done first within the random matrix model. Then it is
shown by semiclassical techniques that the result is due to a cancellation
between diagonal diffractive and off-diagonal periodic-diffractive
contributions. The compensation is a very general phenomenon encoding the
semiclassical content of the optical theorem.Comment: 11 pages, no figure
Self-pulsing effect in chaotic scattering
We study the quantum and classical scattering of Hamiltonian systems whose
chaotic saddle is described by binary or ternary horseshoes. We are interested
in parameters of the system for which a stable island, associated with the
inner fundamental periodic orbit of the system exists and is large, but chaos
around this island is well developed. In this situation, in classical systems,
decay from the interaction region is algebraic, while in quantum systems it is
exponential due to tunneling. In both cases, the most surprising effect is a
periodic response to an incoming wave packet. The period of this self-pulsing
effect or scattering echoes coincides with the mean period, by which the
scattering trajectories rotate around the stable orbit. This period of rotation
is directly related to the development stage of the underlying horseshoe.
Therefore the predicted echoes will provide experimental access to topological
information. We numerically test these results in kicked one dimensional models
and in open billiards.Comment: Submitted to New Journal of Physics. Two movies (not included) and
full-resolution figures are available at http://www.cicc.unam.mx/~mejia
Statistical Properties of Cross-Correlation in the Korean Stock Market
We investigate the statistical properties of the correlation matrix between
individual stocks traded in the Korean stock market using the random matrix
theory (RMT) and observe how these affect the portfolio weights in the
Markowitz portfolio theory. We find that the distribution of the correlation
matrix is positively skewed and changes over time. We find that the eigenvalue
distribution of original correlation matrix deviates from the eigenvalues
predicted by the RMT, and the largest eigenvalue is 52 times larger than the
maximum value among the eigenvalues predicted by the RMT. The
coefficient, which reflect the largest eigenvalue property, is 0.8, while one
of the eigenvalues in the RMT is approximately zero. Notably, we show that the
entropy function with the portfolio risk for the original
and filtered correlation matrices are consistent with a power-law function,
, with the exponent and
those for Asian currency crisis decreases significantly
Signed zeros of Gaussian vector fields-density, correlation functions and curvature
We calculate correlation functions of the (signed) density of zeros of
Gaussian distributed vector fields. We are able to express correlation
functions of arbitrary order through the curvature tensor of a certain abstract
Riemann-Cartan or Riemannian manifold. As an application, we discuss one- and
two-point functions. The zeros of a two-dimensional Gaussian vector field model
the distribution of topological defects in the high-temperature phase of
two-dimensional systems with orientational degrees of freedom, such as
superfluid films, thin superconductors and liquid crystals.Comment: 14 pages, 1 figure, uses iopart.cls, improved presentation, to appear
in J. Phys.
Spin injection across a hybrid heterojunction: Theoretical understanding and experimental approach (invited)
Nonuniversality in level dynamics
Statistical properties of parametric motion in ensembles of Hermitian banded
random matrices are studied. We analyze the distribution of level velocities
and level curvatures as well as their correlation functions in the crossover
regime between three universality classes. It is shown that the statistical
properties of level dynamics are in general non-universal and strongly depend
on the way in which the parametric dynamics is introduced.Comment: 24 pages + 10 figures (not included, avaliable from the author),
submitted to Phys. Rev.
Co-ordination between Rashba spin-orbital interaction and space charge effect and enhanced spin injection into semiconductors
We consider the effect of the Rashba spin-orbital interaction and space
charge in a ferromagnet-insulator/semiconductor/insulator-ferromagnet junction
where the spin current is severely affected by the doping, band structure and
charge screening in the semiconductor. In diffusion region, if the the
resistance of the tunneling barriers is comparable to the semiconductor
resistance, the magnetoresistance of this junction can be greatly enhanced
under appropriate doping by the co-ordination between the Rashba effect and
screened Coulomb interaction in the nonequilibrium transport processes within
Hartree approximation.Comment: 4 pages, 3 figure
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