20,279 research outputs found
Rational approximations in Analytic QCD
We consider the ``modified Minimal Analytic'' (mMA) coupling that involves an
infrared cut to the standard MA coupling. The mMA coupling is a Stieltjes
function and, as a consequence, the paradiagonal Pade approximants converge to
the coupling in the entire -plane except on the time-like semiaxis below
the cut. The equivalence between the narrow width approximation of the
discontinuity function of the coupling, on the one hand, and this Pade
(rational) approximation of the coupling, on the other hand, is shown. We
approximate the analytic analogs of the higher powers of mMA coupling by
rational functions in such a way that the singularity region is respected by
the approximants.Several comparisons, for real and complex arguments ,
between the exact and approximate expressions are made and the speed of
convergence is discussed. Motivated by the success of these approximants, an
improvement of the mMA coupling is suggested, and possible uses in the
reproduction of experimental data are discussed.Comment: 12 pages,9 figures (6 double figures); figs.6-8 corrected due to a
programming error; analysis extended to two IR cutoffs; Introduction
rewritten; to appear in J.Phys.
The entangling side of the Unruh-Hawking effect
We show that the Unruh effect can create net quantum entanglement between
inertial and accelerated observers depending on the choice of the inertial
state. This striking result banishes the extended belief that the Unruh effect
can only destroy entanglement and furthermore provides a new and unexpected
source for finding experimental evidence of the Unruh and Hawking effects.Comment: 4 pages, 4 figures. Added Journal referenc
Efficient time series detection of the strong stochasticity threshold in Fermi-Pasta-Ulam oscillator lattices
In this work we study the possibility of detecting the so-called strong
stochasticity threshold, i.e. the transition between weak and strong chaos as
the energy density of the system is increased, in anharmonic oscillator chains
by means of the 0-1 test for chaos. We compare the result of the aforementioned
methodology with the scaling behavior of the largest Lyapunov exponent computed
by means of tangent space dynamics, that has so far been the most reliable
method available to detect the strong stochasticity threshold. We find that
indeed the 0-1 test can perform the detection in the range of energy density
values studied. Furthermore, we determined that conventional nonlinear time
series analysis methods fail to properly compute the largest Lyapounov exponent
even for very large data sets, whereas the computational effort of the 0-1 test
remains the same in the whole range of values of the energy density considered
with moderate size time series. Therefore, our results show that, for a
qualitative probing of phase space, the 0-1 test can be an effective tool if
its limitations are properly taken into account.Comment: 5 pages, 2 figures; accepted for publication in Physical Review
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