Breakup of three particles within the adiabatic expansion method

General expressions for the breakup cross sections in the lab frame for $1+2$ reactions are given in terms of the hyperspherical adiabatic basis. The three-body wave function is expanded in this basis and the corresponding hyperradial functions are obtained by solving a set of second order differential equations. The ${\cal S}$-matrix is computed by using two recently derived integral relations. Even though the method is shown to be well suited to describe $1+2$ processes, there are nevertheless particular configurations in the breakup channel (for example those in which two particles move away close to each other in a relative zero-energy state) that need a huge number of basis states. This pathology manifests itself in the extremely slow convergence of the breakup amplitude in terms of the hyperspherical harmonic basis used to construct the adiabatic channels. To overcome this difficulty the breakup amplitude is extracted from an integral relation as well. For the sake of illustration, we consider neutron-deuteron scattering. The results are compared to the available benchmark calculations

Recombination rates from potential models close to the unitary limit

We investigate universal behavior in the recombination rate of three bosons close to threshold. Using the He-He system as a reference, we solve the three-body Schr\"odinger equation above the dimer threshold for different potentials having large values of the two-body scattering length $a$. To this aim we use the hyperspherical adiabatic expansion and we extract the $S$-matrix through the integral relations recently derived. The results are compared to the universal form, $\alpha\approx 67.1\sin^2[s_0\ln(\kappa_*a)+\gamma]$, for different values of $a$ and selected values of the three-body parameter $\kappa_*$. A good agreement with the universal formula is obtained after introducing a particular type of finite-range corrections, which have been recently proposed by two of the authors in Ref.[1]. Furthermore, we analyze the validity of the above formula in the description of a very different system: neutron-neutron-proton recombination. Our analysis confirms the universal character of the process in systems of very different scales having a large two-body scattering length

Influence of Dislocations in Thomson's Problem

We investigate Thomson's problem of charges on a sphere as an example of a system with complex interactions. Assuming certain symmetries we can work with a larger number of charges than before. We found that, when the number of charges is large enough, the lowest energy states are not those with the highest symmetry. As predicted previously by Dodgson and Moore, the complex patterns in these states involve dislocation defects which screen the strains of the twelve disclinations required to satisfy Euler's theorem.Comment: 9 pages, 4 figures in gif format. Original PS files can be obtained in http://fermi.fcu.um.es/thomso

Numerical study of relaxation in electron glasses

We perform a numerical simulation of energy relaxation in three-dimensional electron glasses in the strongly localized regime at finite temperatures. We consider systems with no interactions, with long-range Coulomb interactions and with short-range interactions, obtaining a power law relaxation with an exponent of 0.15, which is independent of the parameters of the problem and of the type of interaction. At very long times, we always find an exponential regime whose characteristic time strongly depends on temperature, system size, interaction type and localization radius. We extrapolate the longest relaxation time to macroscopic sizes and, for interacting samples, obtain values much larger than the measuring time. We finally study the number of electrons participating in the relaxation processes of very low energy configurations.Comment: 6 eps figures. To be published in Phys. Rev.

Integral relations and the adiabatic expansion method for 1+2 reactions above the breakup threshold: Helium trimers with soft-core potentials

The integral relations formalism introduced in \cite{bar09,rom11}, and designed to describe 1+$N$ reactions, is extended here to collision energies above the threshold for the target breakup. These two relations are completely general, and in this work they are used together with the adiabatic expansion method for the description of 1+2 reactions. The neutron-deuteron breakup, for which benchmark calculations are available, is taken as a test of the method. The s-wave collision between the $^4$He atom and $^4$He$_2$ dimer above the breakup threshold and the possibility of using soft-core two-body potentials plus a short-range three-body force will be investigated. Comparisons to previous calculations for the three-body recombination and collision dissociation rates will be shown.Comment: To be published in Physical Review

Classical Analog of Electromagnetically Induced Transparency

We present a classical analog for Electromagnetically Induced Transparency (EIT). In a system of just two coupled harmonic oscillators subject to a harmonic driving force we can reproduce the phenomenology observed in EIT. We describe a simple experiment performed with two linearly coupled RLC circuits which can be taught in an undergraduate laboratory class.Comment: 6 pages, two-column, 6 figures, submitted to the Am. J. Phy

Probabilistic Inference from Arbitrary Uncertainty using Mixtures of Factorized Generalized Gaussians

This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both the joint probability density of the variables and the likelihood function of the (objective or subjective) observation are approximated by a special mixture model, in such a way that any desired conditional distribution can be directly obtained without numerical integration. We have developed an extended version of the expectation maximization (EM) algorithm to estimate the parameters of mixture models from uncertain training examples (indirect observations). As a consequence, any piece of exact or uncertain information about both input and output values is consistently handled in the inference and learning stages. This ability, extremely useful in certain situations, is not found in most alternative methods. The proposed framework is formally justified from standard probabilistic principles and illustrative examples are provided in the fields of nonparametric pattern classification, nonlinear regression and pattern completion. Finally, experiments on a real application and comparative results over standard databases provide empirical evidence of the utility of the method in a wide range of applications

Photoconductance of a submicron oxidized line in surface conductive single crystalline diamond

We report on sub-bandgap optoelectronic phenomena of hydrogen-terminated diamond patterned with a submicron oxidized line. The line acts as an energy barrier for the two-dimensional hole gas located below the hydrogenated diamond surface. A photoconductive gain of the hole conductivity across the barrier is measured for sub-bandgap illumination. The findings are consistent with photogenerated electrons being trapped in defect levels within the barrier. We discuss the spatial and energetic characteristics of the optoelectronic phenomena, as well as possible photocurrent effects