215 research outputs found
An approach to Mel'nikov theory in celestial mechanics
Using a completely analytic procedure - based on a suitable extension of a
classical method - we discuss an approach to the Poincar\'e-Mel'nikov theory,
which can be conveniently applied also to the case of non-hyperbolic critical
points, and even if the critical point is located at the infinity. In this
paper, we concentrate our attention on the latter case, and precisely on
problems described by Kepler-like potentials in one or two degrees of freedom,
in the presence of general time-dependent perturbations. We show that the
appearance of chaos (possibly including Arnol'd diffusion) can be proved quite
easily and in a direct way, without resorting to singular coordinate
transformations, such as the McGehee or blowing-up transformations. Natural
examples are provided by the classical Gyld\'en problem, originally proposed in
celestial mechanics, but also of interest in different fields, and by the
general 3-body problem in classical mechanics.Comment: LaTeX, no figure
Symmetric Periodic Solutions of the Anisotropic Manev Problem
We consider the Manev Potential in an anisotropic space, i.e., such that the
force acts differently in each direction. Using a generalization of the
Poincare' continuation method we study the existence of periodic solutions
for weak anisotropy. In particular we find that the symmetric periodic orbits
of the Manev system are perturbed to periodic orbits in the anisotropic
problem.Comment: Late
Seven-body central configurations: a family of central configurations in the spatial seven-body problem
The main result of this paper is the existence of a new family of central
configurations in the Newtonian spatial seven-body problem. This family is
unusual in that it is a simplex stacked central configuration, i.e the bodies
are arranged as concentric three and two dimensional simplexes.Comment: 15 pages 5 figure
Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities
We examine in detail the relative equilibria in the four-vortex problem where
two pairs of vortices have equal strength, that is, \Gamma_1 = \Gamma_2 = 1 and
\Gamma_3 = \Gamma_4 = m where m is a nonzero real parameter. One main result is
that for m > 0, the convex configurations all contain a line of symmetry,
forming a rhombus or an isosceles trapezoid. The rhombus solutions exist for
all m but the isosceles trapezoid case exists only when m is positive. In fact,
there exist asymmetric convex configurations when m < 0. In contrast to the
Newtonian four-body problem with two equal pairs of masses, where the symmetry
of all convex central configurations is unproven, the equations in the vortex
case are easier to handle, allowing for a complete classification of all
solutions. Precise counts on the number and type of solutions (equivalence
classes) for different values of m, as well as a description of some of the
bifurcations that occur, are provided. Our techniques involve a combination of
analysis and modern and computational algebraic geometry
Tight-binding study of the influence of the strain on the electronic properties of InAs/GaAs quantum dots
We present an atomistic investigation of the influence of strain on the
electronic properties of quantum dots (QD's) within the empirical tight-binding (ETB) model with interactions up to 2nd nearest neighbors
and spin-orbit coupling. Results for the model system of capped pyramid-shaped
InAs QD's in GaAs, with supercells containing atoms are presented and
compared with previous empirical pseudopotential results. The good agreement
shows that ETB is a reliable alternative for an atomistic treatment. The strain
is incorporated through the atomistic valence force field model. The ETB
treatment allows for the effects of bond length and bond angle deviations from
the ideal InAs and GaAs zincblende structure to be selectively removed from the
electronic-structure calculation, giving quantitative information on the
importance of strain effects on the bound state energies and on the physical
origin of the spatial elongation of the wave functions. Effects of dot-dot
coupling have also been examined to determine the relative weight of both
strain field and wave function overlap.Comment: 22 pages, 7 figures, submitted to Phys. Rev. B (in press) In the
latest version, added Figs. 3 and 4, modified Fig. 5, Tables I and II,.and
added new reference
Multiband tight-binding theory of disordered ABC semiconductor quantum dots: Application to the optical properties of alloyed CdZnSe nanocrystals
Zero-dimensional nanocrystals, as obtained by chemical synthesis, offer a
broad range of applications, as their spectrum and thus their excitation gap
can be tailored by variation of their size. Additionally, nanocrystals of the
type ABC can be realized by alloying of two pure compound semiconductor
materials AC and BC, which allows for a continuous tuning of their absorption
and emission spectrum with the concentration x. We use the single-particle
energies and wave functions calculated from a multiband sp^3 empirical
tight-binding model in combination with the configuration interaction scheme to
calculate the optical properties of CdZnSe nanocrystals with a spherical shape.
In contrast to common mean-field approaches like the virtual crystal
approximation (VCA), we treat the disorder on a microscopic level by taking
into account a finite number of realizations for each size and concentration.
We then compare the results for the optical properties with recent experimental
data and calculate the optical bowing coefficient for further sizes
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