1,321 research outputs found
Fourier methods for smooth distribution function estimation
In this paper we show how to use Fourier transform methods to analyze the
asymptotic behavior of kernel distribution function estimators. Exact
expressions for the mean integrated squared error in terms of the
characteristic function of the distribution and the Fourier transform of the
kernel are employed to obtain the limit value of the optimal bandwidth sequence
in its greatest generality. The assumptions in our results are mild enough so
that they are applicable when the kernel used in the estimator is a
superkernel, or even the sinc kernel, and this allows to extract some
interesting consequences, as the existence of a class of distributions for
which the kernel estimator achieves a first-order improvement in efficiency
over the empirical distribution function.Comment: 12 pages, 2 figure
Homoclinic Signatures of Dynamical Localization
It is demonstrated that the oscillations in the width of the momentum
distribution of atoms moving in a phase-modulated standing light field, as a
function of the modulation amplitude, are correlated with the variation of the
chaotic layer width in energy of an underlying effective pendulum. The maximum
effect of dynamical localization and the nearly perfect delocalization are
associated with the maxima and minima, respectively, of the chaotic layer
width. It is also demonstrated that kinetic energy is conserved as an almost
adiabatic invariant at the minima of the chaotic layer width, and that the
system is accurately described by delta-kicked rotors at the zeros of the
Bessel functions J_0 and J_1. Numerical calculations of kinetic energy and
Lyapunov exponents confirm all the theoretical predictions.Comment: 7 pages, 4 figures, enlarged versio
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