Voronoi Cell Patterns: theoretical model and applications

We use a simple fragmentation model to describe the statistical behavior of the Voronoi cell patterns generated by a set of points in 1D and in 2D. In particular, we are interested in the distribution of sizes of these Voronoi cells. Our model is completely defined by two probability distributions in 1D and again in 2D, the probability to add a new point inside an existing cell and the probability that this new point is at a particular position relative to the preexisting point inside this cell. In 1D the first distribution depends on a single parameter while the second distribution is defined through a fragmentation kernel; in 2D both distributions depend on a single parameter. The fragmentation kernel and the control parameters are closely related to the physical properties of the specific system under study. We use our model to describe the Voronoi cell patterns of several systems. Specifically, we study the island nucleation with irreversible attachment, the 1D car parking problem, the formation of second-level administrative divisions, and the pattern formed by the Paris M\'etro stations.Comment: 12 pages, 9 figure

The role of excitons and trions on electron spin polarization in quantum wells

We have studied the time evolution of the electron spin polarization under continuous photoexcitation in remotely n-doped semiconductor quantum wells. The doped region allows us to get the necessary excess of free electrons to form trions. We have considered electron resonant photoexcitation at free, exciton and trion electron energy levels. Also, we have studied the relative effect of photoexcitation energy density and doping concentration. In order to obtain the two-dimensional density evolution of the different species, we have performed dynamic calculations through the matrix density formalism. Our results indicate that photoexcitation of free electron level leads to a higher spin polarization. Also, we have found that increasing the photoexcitation energy or diminishing the doping enhances spin polarization.Comment: 30 pages, 11 figures, 1 tabl

Evaluation of the ππ\pi\pi scattering amplitude in the σ\sigma-channel at finite density

The $\pi\pi$ scattering amplitude in the $\sigma$-channel is studied at finite baryonic density in the framework of a chiral unitary approach which successfully reproduces the meson meson phase shifts and generates the $f_0$ and $\sigma$ resonances in vacuum. We address here a new variety of mechanisms recently suggested to modify the $\pi\pi$ interaction in the medium, as well as the role of the $s-$wave selfenergy, in addition to the $p-$wave, in the dressing of the pion propagators.Comment: 26 pages, 17 figure

Nonlinear spin-polarized transport through a ferromagnetic domain wall

A domain wall separating two oppositely magnetized regions in a ferromagnetic semiconductor exhibits, under appropriate conditions, strongly nonlinear I-V characteristics similar to those of a p-n diode. We study these characteristics as functions of wall width and temperature. As the width increases or the temperature decreases, direct tunneling between the majority spin bands decreases the effectiveness of the diode. This has important implications for the zero-field quenched resistance of magnetic semiconductors and for the design of a recently proposed spin transistor.Comment: 5 pages, 3 figure

Quasiparticle Breakdown and Spin Hamiltonian of the Frustrated Quantum Pyrochlore Yb2_2Ti2_2O7_7 in Magnetic Field

The frustrated pyrochlore magnet Yb$_2$Ti$_2$O$_7$ has the remarkable property that it orders magnetically, but has no propagating magnons over wide regions of the Brillouin zone. Here we use inelastic neutron scattering to follow how the spectrum evolves in cubic-axis magnetic fields. At high fields we observe in addition to dispersive magnons also a two-magnon continuum, which grows in intensity upon reducing the field and overlaps with the one-magnon states at intermediate fields leading to strong renormalization of the dispersion relations, and magnon decays. Using heat capacity measurements we find that the low and high field regions are smoothly connected with no sharp phase transition, with the spin gap increasing monotonically in field. Through fits to an extensive data set we re-evaluate the spin Hamiltonian finding dominant quantum exchange terms, which we propose are responsible for the anomalously strong fluctuations and quasiparticle breakdown effects observed at low fields.Comment: 5 pages main text + 19 pages supplemental materia

Trion dynamics in coupled double quantum wells. Electron density effects

We have studied the coherent dynamics of injected electrons when they are either free or bounded both in excitons and in trions (charged excitons). We have considered a remotely doped asymmetric double quantum well where an excess of free electrons and the direct created excitons generate trions. We have used the matrix density formalism to analyze the electron dynamics for different concentration of the three species. Calculations show a significant modification of the free electron inter-sublevel oscillations cWe have studied the coherent dynamics of injected electrons when they are aused by electrons bound in excitons and trions. Based on the present calculations we propose a method to detect trions through the emitted electromagnetic radiation or the current density.Comment: 14 pages, 13 figure