Anderson-like Transition for a Class of Random Sparse Models in d >= 2 Dimensions

We show that the Kronecker sum of d >= 2 copies of a random one-dimensional sparse model displays a spectral transition of the type predicted by Anderson, from absolutely continuous around the center of the band to pure point around the boundaries. Possible applications to physics and open problems are discussed briefly.

Conceptual problem for noncommutative inflation and the new approach for nonrelativistic inflationary equation of state

In a previous paper, we connected the phenomenological noncommutative inflation of Alexander, Brandenberger and Magueijo [ Phys. Rev. D 67 081301 (2003)] and Koh and Brandenberger [ J. Cosmol. Astropart Phys. 2007 21 ()] with the formal representation theory of groups and algebras and analyzed minimal conditions that the deformed dispersion relation should satisfy in order to lead to a successful inflation. In that paper, we showed that elementary tools of algebra allow a group-like procedure in which even Hopf algebras (roughly the symmetries of noncommutative spaces) could lead to the equation of state of inflationary radiation. Nevertheless, in this paper, we show that there exists a conceptual problem with the kind of representation that leads to the fundamental equations of the model. The problem comes from an incompatibility between one of the minimal conditions for successful inflation (the momentum of individual photons being bounded from above) and the Fock-space structure of the representation which leads to the fundamental inflationary equations of state. We show that the Fock structure, although mathematically allowed, would lead to problems with the overall consistency of physics, like leading to a problematic scattering theory, for example. We suggest replacing the Fock space by one of two possible structures that we propose. One of them relates to the general theory of Hopf algebras (here explained at an elementary level) while the other is based on a representation theorem of von Neumann algebras (a generalization of the Clebsch-Gordan coefficients), a proposal already suggested by us to take into account interactions in the inflationary equation of state.

Resonances in Mie scattering by an inhomogeneous atomic cloud

Despite the quantum nature of the process, collective scattering by dense cold samples of two-level atoms can be interpreted classically describing the sample as a macroscopic object with a complex refractive index. We demonstrate that resonances in Mie theory can be easily observable in the cooperative scattering by tuning the frequency of the incident laser field or the atomic number. The solution of the scattering problem is obtained for spherical atomic clouds who have the parabolic density characteristic of BECs, and the cooperative radiation pressure force calculated exhibits resonances in the cloud displacement for dense clouds. At odds with uniform clouds which show a complex structure including narrow peaks, these densities show resonances, yet only under the form of quite regular and contrasted oscillations. Copyright (C) EPLA, 2012

Functionalization of gold and silver nanoparticles with diphenyl dichalcogenides probed by surface enhanced Raman scattering

This paper describes a surface-enhanced Raman scattering (SERS) systematic investigation regarding the functionalization of gold (Au) and silver (Ag) nanoparticles with diphenyl dichalcogenides, i.e. diphenyl disulfide, diphenyl diselenide, and diphenyl ditelluride. Our results showed that, in all cases, functionalization took place with the cleavage of the chalcogenchalcogen bond on the surface of the metal. According to our density functional theory calculations, the molecules assumed a tilted orientation with respect to the metal surface for both Au and Ag, in which the angle of the phenyl ring relative to the metallic surface decreased as the mass of the chalcogen atom increased. The detected differences in the ordinary Raman and SERS spectra were assigned to the distinct stretching frequencies of the carbonchalcogen bond and its relative contribution to the ring vibrational modes. In addition, the SERS spectra showed that there was no significant interaction between the phenyl ring and the surface, in agreement with the tilted orientation observed from our density functional theory calculations. The results described herein indicate that diphenyl dichalcogenides can be successfully employed as starting materials for the functionalization of Au nanoparticles with organosulfur, organoselenium, and organotellurium compounds. On the other hand, diphenyl disulfide and diphenyl diselenide could be employed for the functionalization of Ag nanoparticles, while the partial oxidation of the organotellurium unit could be detected on the Ag surface. Copyright (C) 2011 John Wiley & Sons, Ltd.