Segregation in the Falicov--Kimball Model

The Falicov–Kimball model is a simple quantum lattice model that describes light and heavy electrons interacting with an on-site repulsion; alternatively, it is a model of itinerant electrons and fixed nuclei. It can be seen as a simplification of the Hubbard model; by neglecting the kinetic (hopping) energy of the spin up particles, one gets the Falicov–Kimball model. We show that away from half-filling, i.e. if the sum of the densities of both kinds of particles differs from 1, the particles segregate at zero temperature and for large enough repulsion. In the language of the Hubbard model, this means creating two regions with a positive and a negative magnetization. Our key mathematical results are lower and upper bounds for the sum of the lowest eigenvalues of the discrete Laplace operator in an arbitrary domain, with Dirichlet boundary conditions. The lower bound consists of a bulk term, independent of the shape of the domain, and of a term proportional to the boundary. Therefore, one lowers the kinetic energy of the itinerant particles by choosing a domain with a small boundary. For the Falicov- Kimball model, this corresponds to having a single “compact” domain that has no heavy particles. Received: 21 June 2001 / Accepted: 4 January 2002     

Time Evolution of Vibration-Induced Excited State Decay

A simple model consisting of two electronic levels and one vibrational mode (phonon) was theoretically studied. The electronic-vibrational interaction was linear in the vibrational displacement. The vibrational mode was taken in the harmonic approximation and was attached to the thermal bath formed by the ambient environment. The kinetic constants of the vibrational dissipation were of the second order in the vibrational-bath coupling and were taken in the Markovian limit. Although, depending on the parameters of the model, different curves of the non-radiative vibration-induced excited state decay were obtained, in general, three time intervals, corresponding to different physical behaviour, were found. In the short-time interval, small oscillations superimposed on the excited state decay were observed. They were determined by the vibrational frequency and influenced by electronic-vibrational coupling. In the middle-time interval, almost quasi-exponential decay was detected; its rate constant increased with stronger electronic-vibrational interaction and speed of vibrational relaxation. In the long-time interval, the decay was very slow and, under special conditions, even an asymptotic non-zero excited state population was observed. Its value increased with the strength of the off-diagonal electron-vibrational coupling. Links of the parameters of the model with quantum chemical terms were estimated.     

Towards the Evaluation of the Relevant Degrees of Freedom in Nonlinear Partial Differential Equations

We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical method providing the fundamental concepts of a numerical algorithm applicable to various dynamical systems. We examine dynamical scaling characteristics in the short-time and the long-time evolution regime providing only a reduced number of degrees of freedom to the evolution process.     

GaAsN/AlAs/AlGaAs double barrier quantum wells grown by molecular beam epitaxy as an alternative to infrared absorption below 4 μm

In this work, we report on the design, growth and characterization of GaAsN/AlAs/AlGaAs double barrier quantum well infrared detectors to achieve intraband absorption below 4 μm. Due to the high effective mass of N-dilute alloys, it is common for these N-containing double barrier quantum well structures to have more than one bound state within the quantum well, enabling the possibility of achieving multispectral absorption from these confined levels to the quasi-bound. Based on a transfer matrix calculation we will study the influence of the potential parameters, in particular the well width and the introduction of a GaAs spacer layer in between the N-well and the AlAs barriers. We will compare the case in which there are two confined levels with the case in which only one level is bound, like in the conventional AlGaAs/AlAs/GaAs structures. On the basis of the simulation, we have grown and characterized some N-containing double barrier detectors. Moreover, an optimization of the post-growth annealing treatments of the GaAsN quantum well structures has also been performed. Finally, room temperature absorption measurements of both as-grown and annealed samples are presented and analyzed.     

Une nouvelle méthode de raffinement de maillage spatio-temporel pour l'équation des ondes

In the present Note we introduce an extension of the conservative space–time mesh refinement method presented by Fouquet et al. We also propose a post-treatment of the solution that reduces the spurious phenomena due to the non-conformity between the time meshes. A reinterpretation of the equations in terms of new unknowns leads to a new scheme with second order consistent coupling equations. Numerical experiments in 2D and a plane wave analysis for the 1D model show that the method is second order accurate for an arbitrary refinement. To cite this article: J. Rodríguez, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Design of an experimental procedure for energy evaluation from biomass

The rational and sustainable exploitation of nature resources is one of the priority objectives of our society. In this article a method is proposed to evaluate and exploit the energetic resources contained in different forest formations. This method is based on the use of a combustion bomb calorimeter to determine the calorific values of the different samples studied. These results were complemented with chemical analysis of the samples and with environmental and geomorphological studies of the zones were samples were taken. The results obtained during the last 3 years for the residual biomass originated from the forest formations existing in Galicia ensure the reliability and usefulness of the method that can be extended to any forest formation all over the world.     

Extensions of Modules over Schur Algebras, Symmetric Groups and Hecke Algebras

We study the relation between the cohomology of general linear and symmetric groups and their respective quantizations, using Schur algebras and standard homological techniques to build appropriate spectral sequences. As our methods fit inside a much more general context within the theory of finite-dimensional algebras, we develop our results first in that general setting, and then specialize to the above situations. From this we obtain new proofs of several known results in modular representation theory of symmetric groups. Moreover, we reduce certain questions about computing extensions for symmetric groups and Hecke algebras to questions about extensions for general linear groups and their quantizations.