12,934 research outputs found
Topology, connectivity and electronic structure of C and B cages and the corresponding nanotubes
After a brief discussion of the structural trends which appear with
increasing number of atoms in B cages, a one-to one correspondence between the
connectivity of B cages and C cage structures will be proposed. The electronic
level spectra of both systems from Hartree-Fock calculations is given and
discussed. The relation of curvature introduced into an originally planar
graphitic fragment to pentagonal 'defects' such as are present in
buckminsterfullerene is also briefly treated.
A study of the structure and electronic properties of B nanotubes will then
be introduced. We start by presenting a solution of the free-electron network
approach for a 'model boron' planar lattice with local coordination number 6.
In particular the dispersion relation E(k) for the pi-electron bands, together
with the corresponding electronic Density Of States (DOS), will be exhibited.
This is then used within the zone folding scheme to obtain information about
the electronic DOS of different nanotubes obtained by folding this model boron
sheet.
To obtain the self-consistent potential in which the valence electrons move
in a nanotube, 'the March model' in its original form was invoked and results
are reported for a carbon nanotube.
Finally, heterostructures, such as BN cages and fluorinated
buckminsterfullerene, will be briefly treated, the new feature here being
electronegativity difference.Comment: 22 pages (revtex4) 12 figure
Integral equation for inhomogeneous condensed bosons generalizing the Gross-Pitaevskii differential equation
We give here the derivation of a Gross-Pitaevskii--type equation for
inhomogeneous condensed bosons. Instead of the original Gross-Pitaevskii
differential equation, we obtain an integral equation that implies less
restrictive assumptions than are made in the very recent study of Pieri and
Strinati [Phys. Rev. Lett. 91 (2003) 030401]. In particular, the Thomas-Fermi
approximation and the restriction to small spatial variations of the order
parameter invoked in their study are avoided.Comment: Phys. Rev. A (accepted
Symmetry, winding number and topological charge of vortex solitons in discrete-symmetry media
We determine the functional behavior near the discrete rotational symmetry
axis of discrete vortices of the nonlinear Schr\"odinger equation. We show that
these solutions present a central phase singularity whose charge is restricted
by symmetry arguments. Consequently, we demonstrate that the existence of
high-charged discrete vortices is related to the presence of other off-axis
phase singularities, whose positions and charges are also restricted by
symmetry arguments. To illustrate our theoretical results, we offer two
numerical examples of high-charged discrete vortices in photonic crystal fibers
showing hexagonal discrete rotational invariance.Comment: 6 pages, 2 figure
Sharp crossover from composite fermionization to phase separation in mesoscopic mixtures of ultracold bosons
We show that a two-component mixture of a few repulsively interacting
ultracold atoms in a one-dimensional trap possesses very different quantum
regimes and that the crossover between them can be induced by tuning the
interactions in one of the species. In the composite fermionization regime,
where the interactions between both components are large, none of the species
show large occupation of any natural orbital. Our results show that by
increasing the interaction in one of the species, one can reach the
phase-separated regime. In this regime, the weakly interacting component stays
at the center of the trap and becomes almost fully phase coherent, while the
strongly interacting component is displaced to the edges of the trap. The
crossover is sharp, as observed in the in the energy and the in the largest
occupation of a natural orbital of the weakly interacting species. Such a
transition is a purely mesoscopic effect which disappears for large atom
numbers.Comment: 5 pages, 3 figure
Quantum correlations and spatial localization in one-dimensional ultracold bosonic mixtures
We present the complete phase diagram for one-dimensional binary mixtures of
bosonic ultracold atomic gases in a harmonic trap. We obtain exact results with
direct numerical diagonalization for small number of atoms, which permits us to
quantify quantum many-body correlations. The quantum Monte Carlo method is used
to calculate energies and density profiles for larger system sizes. We study
the system properties for a wide range of interaction parameters. For the
extreme values of these parameters, different correlation limits can be
identified, where the correlations are either weak or strong. We investigate in
detail how the correlation evolve between the limits. For balanced mixtures in
the number of atoms in each species, the transition between the different
limits involves sophisticated changes in the one- and two-body correlations.
Particularly, we quantify the entanglement between the two components by means
of the von Neumann entropy. We show that the limits equally exist when the
number of atoms is increased, for balanced mixtures. Also, the changes in the
correlations along the transitions among these limits are qualitatively
similar. We also show that, for imbalanced mixtures, the same limits with
similar transitions exist. Finally, for strongly imbalanced systems, only two
limits survive, i.e., a miscible limit and a phase-separated one, resembling
those expected with a mean-field approach.Comment: 18 pages, 8 figure
Probabilistic evaluation of n traces with no putative source: A likelihood ratio based approach in an investigative framework
Analysis of marks recovered from different crime scenes can be useful to detect a linkage between criminal cases, even though a putative source for the recovered traces is not available. This particular circumstance is often encountered in the early stage of investigations and thus, the evaluation of evidence association may provide useful information for the investigators. This association is evaluated here from a probabilistic point of view: a likelihood ratio based approach is suggested in order to quantify the strength of the evidence of trace association in the light of two mutually exclusive propositions, namely that the n traces come from a common source or from an unspecified number of sources. To deal with this kind of problem, probabilistic graphical models are used, in form of Bayesian networks and object-oriented Bayesian networks, allowing users to intuitively handle with uncertainty related to the inferential problem
Information entropy and nucleon correlations in nuclei
The information entropies in coordinate and momentum spaces and their sum
(, , ) are evaluated for many nuclei using "experimental"
densities or/and momentum distributions. The results are compared with the
harmonic oscillator model and with the short-range correlated distributions. It
is found that depends strongly on and does not depend very much
on the model. The behaviour of is opposite. The various cases we consider
can be classified according to either the quantity of the experimental data we
use or by the values of , i.e., the increase of the quality of the density
and of the momentum distributions leads to an increase of the values of . In
all cases, apart from the linear relation , the linear relation
also holds. V is the mean volume of the nucleus. If is
considered as an ensemble entropy, a relation between or and the
ensemble volume can be found. Finally, comparing different electron scattering
experiments for the same nucleus, it is found that the larger the momentum
transfer ranges, the larger the information entropy is. It is concluded that
could be used to compare different experiments for the same nucleus and to
choose the most reliable one.Comment: 14 pages, 4 figures, 2 table
A Three Dimensional Lattice of Ion Traps
We propose an ion trap configuration such that individual traps can be
stacked together in a three dimensional simple cubic arrangement. The isolated
trap as well as the extended array of ion traps are characterized for different
locations in the lattice, illustrating the robustness of the lattice of traps
concept. Ease in the addressing of ions at each lattice site, individually or
simultaneously, makes this system naturally suitable for a number of
experiments. Application of this trap to precision spectroscopy, quantum
information processing and the study of few particle interacting system are
discussed.Comment: 4 pages, 4 Figures. Fig 1 appears as a composite of 1a, 1b, 1c and
1d. Fig 2 appears as a composite of 2a, 2b and 2
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