Positivity of Lyapunov Exponents for a Continuous Matrix-Valued Anderson Model

We study a continuous matrix-valued Anderson-type model. Both leading Lyapunov exponents of this model are proved to be positive and distinct for all energies in (2, +∞) except those in a discrete set, which leads to absence of absolutely continuous spectrum in (2, +∞). This result is an improvement of a previous result with Stolz. The methods, based upon a result by Breuillard and Gelander on dense subgroups in semisimple Lie groups, and a criterion by Goldsheid and Margulis, allow for singular Bernoulli distributions.      

Localization for a Matrix-valued Anderson Model

We study localization properties for a class of one-dimensional, matrix-valued, continuous, random Schrödinger operators, acting on $L^2(\mathbb R)\otimes \mathbb C^NWe study localization properties for a class of one-dimensional, matrix-valued, continuous, random Schr?dinger operators, acting on , for arbitrary N ≥ 1. We prove that, under suitable assumptions on the Fürstenberg group of these operators, valid on an interval , they exhibit localization properties on I, both in the spectral and dynamical sense. After looking at the regularity properties of the Lyapunov exponents and of the integrated density of states, we prove a Wegner estimate and apply a multiscale analysis scheme to prove localization for these operators. We also study an example in this class of operators, for which we can prove the required assumptions on the Fürstenberg group. This group being the one generated by the transfer matrices, we can use, to prove these assumptions, an algebraic result on generating dense Lie subgroups in semisimple real connected Lie groups, due to Breuillard and Gelander. The algebraic methods used here allow us to handle with singular distributions of the random parameters.      

Photoelectrochemical study of La2NiO4 synthesized using citrate sol gel method—application for hydrogen photo-production

Journal of Solid State Electrochemistry - The semi conducting properties of La2NiO4 synthesized through sol gel method are studied for the first time using photoelectrochemistry. The X-ray...     

A Matrix-Valued Point Interactions Model

We study a matrix-valued Schrödinger operator with random point interactions. We prove the absence of absolutely continuous spectrum for this operator by proving that, away from a discrete set, its Lyapunov exponents do not vanish. For this we use a criterion by Gol’dsheid and Margulis and we prove the Zariski denseness, in the symplectic group, of the group generated by the transfer matrices. Then we prove estimates on the transfer matrices which lead to the Hölder continuity of the Lyapunov exponents. After proving the existence of the integrated density of states of the operator, we also prove its Hölder continuity by proving a Thouless formula which links the integrated density of states to the sum of the positive Lyapunov exponents.     

Modeling and analysis of birefringence in magneto-optical thin film made by SiO2/ZrO2 doped with ferrite of cobalt

We report the device characteristics of the metal–dielectric high-reflectivity (HR) coated 1.55 μm laterally coupled distributed feedback (DFB) laser with metal surface gratings by using holographic lithography. The HR coating films are composed of Au/Ti/SiO₂. It provides a variety of advantages compared to the uncoated DFB laser on the same processed wafer while there is no degradation on current–voltage characteristics. For 3 μm wide and 300 μm long HR coated DFB laser, it exhibits a maximum output power of ∼17 mW and a threshold current of 14.2 mA at 20°C under continuous-wave mode. It is clear that the threshold current and slope efficiency are improved by 36% and 96%, respectively, due to the reduction of mirror loss. The metal–dielectric HR coating on one facet of DFB laser is found to have significantly increased characteristic temperature (i.e., T ₀∼88 K). Furthermore, the stable single-mode operation with an increased single-mode suppression ratio was achieved.     

Electrochemical characterization of the brownmillerite Ca2Fe2O5+δ synthesized by citrate sol–gel method. Application to photocatalytic H2-production

Journal of Solid State Electrochemistry - The present study focuses on the preparation and electrochemical characterization of the calcium ferrite (Ca2Fe2O5+δ), a semiconductor crystallizing...     

Semiconducting and photoelectrochemical properties of the ilmenite CoTiO3 prepared by wet method and its application for O2 evolution under visible light

Journal of Solid State Electrochemistry - The ilmenite CoTiO3 was synthesized by chemical route, and the decomposition of nitrates was followed by thermal analysis (TG/DTA). The intermediate...     

Transition alumina phases induced by heat treatment of boehmite: An X-ray diffraction and infrared spectroscopy study

During high temperature oxidation of alumina-forming alloys, various transition aluminas are formed before reaching the most stable α-Al₂O₃ phase. In particular, the γ, δ and θ transition aluminas are concerned. Precise studies on the development, the microstructure and the properties of the oxide layers are not straightforward owing to the difficulty to unambiguously distinguish the various polymorphs by X-ray diffraction (XRD) alone. To remove this difficulty, we propose a procedure which combines XRD and infrared (IR) spectroscopy. γ, δ, θ and α-Al₂O₃ phases, prepared by dehydration of aluminium oxihydroxide AlOOH (boehmite), were measured by XRD and IR spectroscopy on all samples. Thus, reference IR spectra were obtained for all alumina phases, as well as an assignment of the main band in agreement with previous studies, and coherent with the structural evolution of various polymorphs. This precise characterization may constitute a basis for further investigations on thin layers of alumina formed under various experimental conditions (temperature, atmosphere, etc.).