Low energy scales of Kondo lattices: mean-field perspective

A review of the low temperature properties of Kondo lattice systems is presented within the mean-field approximation, focusing on the different characteristic energy scales. The Kondo temperature, T_K, and the Fermi liquid coherence energy, T_0, are analyzed as functions of the electronic filling, the shape of the non-interacting density of states, and the concentration of magnetic moments. These two scales can vanish, corresponding to a breakdown of the Kondo effect when an external magnetic field is applied. The Kondo breakdown can also be reached by adding a superexchange term to the Kondo lattice model, which mimics the intersite magnetic correlations neglected at the mean-field level.Comment: 17 pages, 9 figures. Proceedings of the NATO Advanced Research Workshop of Hvar, Croatia (2008

Alternative equation of motion approach to the single-impurity Anderson model

Solving the single-impurity Anderson model (SIAM) is a basic problem of solid state physics. The SIAM model is very important, at present it is also used for systems with quantum impurities, e.g. semiconductor quantum dots and molecular transistors. Its main application is in the scheme of dynamical mean field theory (DMFT) describing strong correlation electron systems. To solve the SIAM problem we use the equation of motion (EOM) Green function approach. In this report we present the novel EOM approximation in which we differentiate the Green function over both time variables. This differs from the commonly used EOM solution by Appelbaum, Penn and Lacroix where the authors take time derivative only over primary time variable. After extending calculations to higher order Green functions we find the new approximate dynamical solution of SIAM. The results are compared with the solutions to the SIAM problem at intermediate Coulomb repulsion U such as the Modified Iterative Perturbation Theory. Our approach is suitable for describing quantum dots.Comment: 6 pages, 3 figure

Heavy-fermion and spin-liquid behavior in a Kondo lattice with magnetic frustration

We study the competition between the Kondo effect and frustrating exchange interactions in a Kondo-lattice model within a large-${\cal N}$ dynamical mean-field theory. We find a T=0 phase transition between a heavy Fermi-liquid and a spin-liquid for a critical value of the exchange $J_c = T_{K}^0$, the single-impurity Kondo temperature. Close to the critical point, the Fermi liquid coherence scale $T^\star$ is strongly reduced and the effective mass strongly enhanced. The regime $T>T^\star$ is characterized by spin-liquid magnetic correlations and non-Fermi-liquid properties. It is suggested that magnetic frustration is a general mechanism which is essential to explain the large effective mass of some metallic compounds such as LiV$_2$O$_4$.Comment: 7 pages, 1 figure. Late

Asymptotics for hitting times

In this paper we characterize possible asymptotics for hitting times in aperiodic ergodic dynamical systems: asymptotics are proved to be the distribution functions of subprobability measures on the line belonging to the functional class {6pt} {-3mm}(A){6mm}F={F:R\to [0,1]:\left\lbrack \matrixF is increasing, null on ]-\infty, 0]; \noalignF is continuous and concave; \noalignF(t)\le t for t\ge 0.\right.}. {6pt} Note that all possible asymptotics are absolutely continuous.Comment: Published at http://dx.doi.org/10.1214/009117904000000883 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Combination of AFM, SKPFM, and SIMS to Study the Corrosion Behavior of S-phase particles in AA2024-T351

The dissolution mechanism of S-phase particles in 2024-T351 aluminum alloy at open-circuit potential in chloride-containing sulfate solutions was investigated using atomic force microscopy (AFM), scanning Kelvin probe force microscopy (SKPFM), and secondary ion mass spectroscopy (SIMS). The combination of the three techniques allowed the correlation between SKPFM measurements and the corrosion behavior of AA2024 to be confirmed, leading to a better understanding of the electrochemical behavior of S-phase particles. A three-step mechanism for the dissolution and accompanying processes occurring near S particles was proposed: (i) preferential aluminum and magnesium dissolution, (ii) galvanic coupling between the copper-enriched particles and the surrounding matrix, leading to an increased passivity of the matrix around the particles, and (iii) copper deposition around the corroded particles

Emile Borel's difficult days in 1941

The German forces occupying Paris arrested Emile Borel and three other members of the Acad\'emie des Sciences in October 1941 and released them about five weeks later. Why? We examine some relevant German and French archives and other sources and propose some hypotheses. In the process, we review how the Occupation was structured and how it dealt with French higher education and some French mathematicians