1,154 research outputs found
New representations of pi and Dirac delta using the nonextensive-statistical-mechanics q-exponential function
We present a generalization of the representation in plane waves of Dirac
delta, , namely
, using the
nonextensive-statistical-mechanics -exponential function,
with , being
any real number, for real values of within the interval .
Concomitantly with the development of these new representations of Dirac delta,
we also present two new families of representations of the transcendental
number . Incidentally, we remark that the -plane wave form which
emerges, namely , is normalizable for , in contrast with the
standard one, , which is not.Comment: 13 pages, 6 figures. Accepted for publication in the Journal of
Mathematical Physics. Some misprints have been eliminate
q-Moments remove the degeneracy associated with the inversion of the q-Fourier transform
It was recently proven [Hilhorst, JSTAT, P10023 (2010)] that the
q-generalization of the Fourier transform is not invertible in the full space
of probability density functions for q > 1. It has also been recently shown
that this complication disappears if we dispose of the q-Fourier transform not
only of the function itself, but also of all of its shifts [Jauregui and
Tsallis, Phys. Lett. A 375, 2085 (2011)]. Here we show that another road exists
for completely removing the degeneracy associated with the inversion of the
q-Fourier transform of a given probability density function. Indeed, it is
possible to determine this density if we dispose of some extra information
related to its q-moments.Comment: 11 pages, 12 figure
q-Generalization of the inverse Fourier transform
A wide class of physical distributions appears to follow the q-Gaussian form,
which plays the role of attractor according to a Central Limit Theorem
generalized in the presence of specific correlations between the relevant
random variables. In the realm of this theorem, a q-generalized Fourier
transform plays an important role. We introduce here a method which univocally
determines a distribution from the knowledge of its q-Fourier transform and
some supplementary information. This procedure involves a recently
q-generalized Dirac delta and the class of functions on which it acts. The
present method conveniently extends the inverse of the standard Fourier
transform, and is therefore expected to be very useful in the study of many
complex systems.Comment: 6 pages, 3 figures. To appear in Physics Letters
Wigner Molecules in Nanostructures
The one-- and two-- particle densities of up to four interacting electrons
with spin, confined within a quasi one--dimensional ``quantum dot'' are
calculated by numerical diagonalization. The transition from a dense
homogeneous charge distribution to a dilute localized Wigner--type electron
arrangement is investigated. The influence of the long range part of the
Coulomb interaction is studied. When the interaction is exponentially cut off
the ``crystallized'' Wigner molecule is destroyed in favor of an inhomogeneous
charge distribution similar to a charge density wave .Comment: 10 pages (excl. Figures), Figures available on request LaTe
Particle creation in an oscillating spherical cavity
We study the creation of massless scalar particles from the quantum vacuum
due to the dynamical Casimir effect by spherical shell with oscillating radius.
In the case of a small amplitude of the oscillation, to solve the infinite set
of coupled differential equations for the instantaneous basis expansion
coefficients we use the method based on the time-dependent perturbation theory
of the quantum mechanics. To the first order of the amplitude we derive the
expressions for the number of the created particles for both parametric
resonance and non-resonance cases.Comment: 8 pages, LaTeX, no figure
Effect of oxygen plasma etching on graphene studied with Raman spectroscopy and electronic transport
We report a study of graphene and graphene field effect devices after
exposure to a series of short pulses of oxygen plasma. We present data from
Raman spectroscopy, back-gated field-effect and magneto-transport measurements.
The intensity ratio between Raman "D" and "G" peaks, I(D)/I(G) (commonly used
to characterize disorder in graphene) is observed to increase approximately
linearly with the number (N(e)) of plasma etching pulses initially, but then
decreases at higher Ne. We also discuss implications of our data for extracting
graphene crystalline domain sizes from I(D)/I(G). At the highest Ne measured,
the "2D" peak is found to be nearly suppressed while the "D" peak is still
prominent. Electronic transport measurements in plasma-etched graphene show an
up-shifting of the Dirac point, indicating hole doping. We also characterize
mobility, quantum Hall states, weak localization and various scattering lengths
in a moderately etched sample. Our findings are valuable for understanding the
effects of plasma etching on graphene and the physics of disordered graphene
through artificially generated defects.Comment: 10 pages, 5 figure
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