The congruence kernel of an arithmetic lattice in a rank one algebraic group over a local field

Let k be a global field and let k_v be the completion of k with respect to v, a non-archimedean place of k. Let \mathbf{G} be a connected, simply-connected algebraic group over k, which is absolutely almost simple of k_v-rank 1. Let G=\mathbf{G}(k_v). Let \Gamma be an arithmetic lattice in G and let C=C(\Gamma) be its congruence kernel. Lubotzky has shown that C is infinite, confirming an earlier conjecture of Serre. Here we provide complete solution of the congruence subgroup problem for \Gamm$ by determining the structure of C. It is shown that C is a free profinite product, one of whose factors is \hat{F}_{\omega}, the free profinite group on countably many generators. The most surprising conclusion from our results is that the structure of C depends only on the characteristic of k. The structure of C is already known for a number of special cases. Perhaps the most important of these is the (non-uniform) example \Gamma=SL_2(\mathcal{O}(S)), where \mathcal{O}(S) is the ring of S-integers in k, with S=\{v\}, which plays a central role in the theory of Drinfeld modules. The proof makes use of a decomposition theorem of Lubotzky, arising from the action of \Gamma on the Bruhat-Tits tree associated with G.Comment: 27 pages, 5 figures, to appear in J. Reine Angew. Mat

Spectral dependence of photoinduced spin precession in DyFeO3

Spin precession was nonthermally induced by an ultrashort laser pulse in orthoferrite DyFeO3 with a pump-probe technique. Both circularly and linearly polarized pulses led to spin precessions; these phenomena are interpreted as the inverse Faraday effect and the inverse Cotton-Mouton effect, respectively. For both cases, the same mode of spin precession was excited; the precession frequencies and polarization were the same, but the phases of oscillations were different. We have shown theoretically and experimentally that the analysis of phases can distinguish between these two mechanisms. We have demonstrated experimentally that in the visible region, the inverse Faraday effect was dominant, whereas the inverse Cotton-Mouton effect became relatively prominent in the near-infrared region.Comment: 27 pages, 8 figure

Optical Properties of Cu(In, Ga)(S, Se)2 Films for Solar Cells

In this paper, we present structural and optical properties of single-phase Cu(In, Ga)(S, Se)2 alloys, which have been prepared using a novel selenization/sulfurization growth process to react copper-indium-gallium alloy films. The grown scheme differs critically from standard two-step grown processes and was carried out without toxic H2S and H2Se gases. The calculated band gap values for layers with varying sulfur content (i.e. S/(S+Se) = 0.16 and 0.19), determined from optical transmission and reflectance measurements, were found to be 1.17 and 1.23 eV respectively. The low temperature PL measurements also confirmed the shift in the band gap of the CIGSS absorber films with sulfur incorporation. In summary, this reaction process produced single-phase CIGSS thin films with controlled sulfur amount suitable for photovoltaic application

Cadmium-free Thin-Film Cu(In,Ga)Se2(In2S3) Heterophotoelements Fabrication and Properties

The method of heat treatment of metallic Cu–In–Ga layers in the N2 inert atmosphere in the presence of selenium and sulfur vapors was used to grow homogeneous films of Cu(In,Ga)(S,Se)2 alloys onto which the CdS or In2S3 films were deposited and, on the basis of these structures, the thin-film glass/Mo/p-Cu(In,Ga)(S,Se)2/n-(In2S3,CdS)/n-ZnO/Ni–Al photoelements were fabricated. The mechanisms of charge transport and the processes of photosensitivity in the obtained structures subjected to irradiation with natural and linearly polarized light are discussed. The broadband hotosensitivity of thin-film heterophotoelements and the induced photopleochroism were detected; these findings indicate that there is an interference-related blooming of the structures obtained. It is concluded that it is possible to use ecologically safe cadmium-free thin-film heterostructures as high-efficiency photoconverters of solar radiation