12,245 research outputs found
Summation formula inequalities for eigenvalues of the perturbed harmonic oscillator
We derive explicit inequalities for sums of eigenvalues of one-dimensional
Schr\"{o}dinger operators on the whole line. In the case of the perturbed
harmonic oscillator, these bounds converge to the corresponding trace formula
in the limit as the number of eigenvalues covers the whole spectrum.Comment: 15 pages, to appear in Osaka J. Mat
Extreme Value Laws for dynamical systems with countable extremal sets
We consider stationary stochastic processes arising from dynamical systems by
evaluating a given observable along the orbits of the system. We focus on the
extremal behaviour of the process, which is related to the entrance in certain
regions of the phase space, which correspond to neighbourhoods of the maximal
set , i.e. the set of points where the observable is maximised. The
main novelty here is the fact that we consider that the set may
have a countable number of points, which are associated by belonging to the
orbit of a certain point, and may have accumulation points. In order to prove
the existence of distributional limits and study the intensity of clustering,
given by the Extremal Index, we generalise the conditions previously introduced
in \cite{FFT12,FFT15}.Comment: arXiv admin note: text overlap with arXiv:1505.0155
Comment on "Effective of the q-deformed pseudoscalar magnetic field on the charge carriers in graphene"
We point out a misleading treatment in a recent paper published in this
Journal [J. Math. Phys. (2016) 57, 082105] concerning solutions for the
two-dimensional Dirac-Weyl equation with a q-deformed pseudoscalar magnetic
barrier. The authors misunderstood the full meaning of the potential and made
erroneous calculations, this fact jeopardizes the main results in this system.Comment: 7 pages, 2 figure
Polytropic equation of state and primordial quantum fluctuations
We study the primordial Universe in a cosmological model where inflation is
driven by a fluid with a polytropic equation of state . We calculate the dynamics of the scalar factor and build a
Universe with constant density at the origin. We also find the equivalent
scalar field that could create such equation of state and calculate the
corresponding slow-roll parameters. We calculate the scalar perturbations, the
scalar power spectrum and the spectral index.Comment: 16 pages, 4 figure
Nonextensivity in the solar magnetic activity during the increasing phase of solar Cycle 23
In this paper we analyze the behavior of the daily Sunspot Number from the
Sunspot Index Data Center (SIDC), the mean Magnetic Field strength from the
National Solar Observatory/Kitt Peak (NSO/KP) and Total Solar Irradiance means
from Virgo/SoHO, in the context of the --Triplet which emerges within
nonextensive statistical mechanics. Distributions for the mean solar Magnetic
Field show two different behaviors, with a --Gaussian for scales of 1 to 16
days and a Gaussian for scales longer than 32 days. The latter corresponds to
an equilibrium state. Distributions for Total Solar Irradiance also show two
different behaviors (approximately Gaussian) for scales of 128 days and longer,
consistent with statistical equilibrium and --Gaussian for scales 128
days. Distributions for the Sunspot Number show a --Gaussian independent of
timescales, consistent with a nonequilibrium state. The values obtained
("--Triplet",,)
demonstrate that the Gaussian or --Gaussian behavior of the aforementioned
data depends significantly on timescales. These results point to strong
multifractal behavior of the dataset analyzed, with the multifractal level
decreasing from Sunspot Number to Total Solar Irradiance. In addition, we found
a numerically satisfied dual relation between and .Comment: 6 pages, 4 figure
Asymptotic behaviour and numerical approximation of optimal eigenvalues of the Robin Laplacian
We consider the problem of minimising the eigenvalue of the Robin
Laplacian in . Although for and a positive boundary
parameter it is known that the minimisers do not depend on ,
we demonstrate numerically that this will not always be the case and illustrate
how the optimiser will depend on . We derive a Wolf-Keller type result
for this problem and show that optimal eigenvalues grow at most with ,
which is in sharp contrast with the Weyl asymptotics for a fixed domain. We
further show that the gap between consecutive eigenvalues does go to zero as
goes to infinity. Numerical results then support the conjecture that for
each there exists a positive value of such that the eigenvalue is minimised by disks for all and,
combined with analytic estimates, that this value is expected to grow with
Strong evidences for a nonextensive behavior of the rotation period in Open Clusters
Time-dependent nonextensivity in a stellar astrophysical scenario combines
nonextensive entropic indices derived from the modified Kawaler's
parametrization, and , obtained from rotational velocity distribution. These
's are related through a heuristic single relation given by , where is the cluster age. In a nonextensive
scenario, these indices are quantities that measure the degree of
nonextensivity present in the system. Recent studies reveal that the index
is correlated to the formation rate of high-energy tails present in the
distribution of rotation velocity. On the other hand, the index is
determined by the stellar rotation-age relationship. This depends on the
magnetic field configuration through the expression , where
and denote the saturation level of the star magnetic field and its
topology, respectively. In the present study, we show that the connection
is also consistent with 548 rotation period data for single
main-sequence stars in 11 Open Clusters aged less than 1 Gyr. The value of
2.5 from our unsaturated model shows that the mean magnetic field
topology of these stars is slightly more complex than a purely radial field.
Our results also suggest that stellar rotational braking behavior affects the
degree of anti-correlation between and cluster age . Finally, we suggest
that stellar magnetic braking can be scaled by the entropic index .Comment: 6 pages and 2 figures, accepted to EPL on October 17, 201
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