29,337 research outputs found
Localization properties of a tight-binding electronic model on the Apollonian network
An investigation on the properties of electronic states of a tight-binding
Hamiltonian on the Apollonian network is presented. This structure, which is
defined based on the Apollonian packing problem, has been explored both as a
complex network, and as a substrate, on the top of which physical models can
defined. The Schrodinger equation of the model, which includes only nearest
neighbor interactions, is written in a matrix formulation. In the uniform case,
the resulting Hamiltonian is proportional to the adjacency matrix of the
Apollonian network. The characterization of the electronic eigenstates is based
on the properties of the spectrum, which is characterized by a very large
degeneracy. The rotation symmetry of the network and large number of
equivalent sites are reflected in all eigenstates, which are classified
according to their parity. Extended and localized states are identified by
evaluating the participation rate. Results for other two non-uniform models on
the Apollonian network are also presented. In one case, interaction is
considered to be dependent of the node degree, while in the other one, random
on-site energies are considered.Comment: 7pages, 7 figure
Optical spectra of a quantum dot in a microcavity in the nonlinear regime
The optical emission spectrum of a quantum dot in strong coupling with the
single mode of a microcavity is obtained in the nonlinear regime. We study how
exciton-exciton interactions alter the emission spectrum of the system,
bringing the linear Rabi doublet into a multiplet structure that is strongly
dependent on the cavity-exciton energy detuning. We emphasise how nonlinearity
can be used to evidence the genuine quantum nature of the coupling by producing
satellites peaks of the Rabi doublet that originate from the quantized energy
levels of the interactions.Comment: Low quality figures. To be published in Phys. Rev. B. 78 (2008
Generalized entropy arising from a distribution of q-indices
It is by now well known that the Boltzmann-Gibbs (BG) entropy
can be usefully generalized into the
entropy (). Microscopic dynamics determines, given classes of initial
conditions, the occupation of the accessible phase space (or of a
symmetry-determined nonzero-measure part of it), which in turn appears to
determine the entropic form to be used. This occupation might be a uniform one
(the usual {\it equal probability hypothesis} of BG statistical mechanics),
which corresponds to ; it might be a free-scale occupancy, which appears
to correspond to . Since occupancies of phase space more complex than
these are surely possible in both natural and artificial systems, the task of
further generalizing the entropy appears as a desirable one, and has in fact
been already undertaken in the literature. To illustrate the approach, we
introduce here a quite general entropy based on a distribution of -indices
thus generalizing . We establish some general mathematical properties for
the new entropic functional and explore some examples. We also exhibit a
procedure for finding, given any entropic functional, the -indices
distribution that produces it. Finally, on the road to establishing a quite
general statistical mechanics, we briefly address possible generalized
constraints under which the present entropy could be extremized, in order to
produce canonical-ensemble-like stationary-state distributions for Hamiltonian
systems.Comment: 14 pages including 3 figure
Spin-orbit mode transfer via a classical analog of quantum teleportation
We translate the quantum teleportation protocol into a sequence of coherent
operations involving three degrees of freedom of a classical laser beam. The
protocol, which we demonstrate experimentally, transfers the polarisation state
of the input beam to the transverse mode of the output beam. The role of
quantum entanglement is played by a non-separable mode describing the path and
transverse degrees of freedom. Our protocol illustrates the possibility of new
optical applications based on this intriguing classical analogue of quantum
entanglement.Comment: 5 pages, 7 figure
Two field BPS solutions for generalized Lorentz breaking models
In this work we present nonlinear models in two-dimensional space-time of two
interacting scalar fields in the Lorentz and CPT violating scenarios. We
discuss the soliton solutions for these models as well as the question of
stability for them. This is done by generalizing a model recently published by
Barreto and collaborators and also by getting new solutions for the model
introduced by them.Comment: 12 pages, 2 figure
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