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 $2\pi /3$ 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 $S_{BG}=-k\sum_{i=1}^W p_i \ln p_i$ can be usefully generalized into the entropy $S_q=k (1-\sum_{i=1}^Wp_i^{q}) / (q-1)$ ($q\in \mathcal{R}; S_1=S_{BG}$). 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 $q=1$; it might be a free-scale occupancy, which appears to correspond to $q \ne 1$. 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 $q$-indices thus generalizing $S_q$. 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 $q$-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