Support theorems for random Schrödinger operators

In the multi-dimensional case it is shown that the increase of the topological support of the probability measure describing the randomness of potentials implies the increase of the spectrum. In the one-dimensional case the converse statement for the absolutely continuous spectrum is valid. Especially the spectrum (in general dimension) and the absolutely continuous spectrum (in one-dimension) are determined only by the topological support of the random potentials.Research partially supported by the USNSF under grant MCS-81-20833     

Anomalous behavior of the surface state in ferromagnetic superconductors

The effect of the electromagnetic interaction between the persistent current and the magnetic moments to the surface state in ferromagnetic superconductors is studied theoretically. This interaction causes an oscillatory decay of the penetrated magnetic field near the magnetic phase transition temperature. Below a critical temperature, the spontaneous surface magnetization is stabilized by the magnetic field induced by the surface persistent current.     

Ab initio prediction of conduction band spin splitting in zinc blende semiconductors

We use a recently developed self-consistent GW approximation to present systematic ab initio calculations of the conduction band spin splitting in III-V and II-VI zinc blende semiconductors. The spin-orbit interaction is taken into account as a perturbation to the scalar relativistic Hamiltonian. These are the first calculations of conduction band spin splittings based on a quasiparticle approach; and because the self-consistent GW scheme accurately reproduces the relevant band parameters, it is expected to be a reliable predictor of spin splittings. The results are compared to the few available experimental data and a previous calculation based on a model one-particle potential. We also briefly address the widely used k x p parametrization in the context of these results.     

Diffusion and reactions of interstitial oxygen species in amorphous SiO2: A review

This article briefly summarizes the diffusion and reactions of interstitial oxygen species in amorphous SiO₂ (a-SiO₂). The most common form of interstitial oxygen species is oxygen molecule (O₂), which is sensitively detectable via its characteristic infrared photoluminescence (PL) at 1272 nm. The PL observation of interstitial O₂ provides key data to verify various processes related to interstitial oxygen species: the dominant role of interstitial O₂ in long-range oxygen transport in a-SiO₂; formation of the Frenkel defect pair (Si–Si bond and interstitial oxygen atom, O⁰) by dense electronic excitation; efficient photolysis of interstitial O₂ into O⁰ with F₂ laser light (λ = 157 nm, hν = 7.9 eV); and creation of interstitial ozone molecule via reaction of interstitial O₂ with photogenerated O⁰. The efficient formation of interstitial O⁰ by F₂ laser photolysis makes it possible to investigate the mobility, optical absorption, and chemical reactions of interstitial O⁰. The observed properties of O⁰ are consistent with the model that O⁰ takes the configuration of Si–O–O–Si bond. Interstitial O₂ and O⁰ react with dangling bonds, oxygen vacancies, and chloride groups in a-SiO₂. Reactions of interstitial O₂ and O⁰ with mobile interstitial hydrogen species produce interstitial water molecules and hydroperoxy radicals. Interstitial hydroxyl radicals are formed by F₂ laser photolysis of interstitial water molecules.     

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??This article provides the readers with an introduction to the spectral theory of ergodic one dimensional Schrodinger operators. The theorems developed by the author are mainly discussed and their proofs are given in detail.     

A Mechanistic Dichotomy in Two-Electron Reduction of Dioxygen Catalyzed by N,N’-Dimethylated Porphyrin Isomers

Selective two-electron reduction of dioxygen (O₂) to hydrogen peroxide (H₂O₂) has been achieved by two saddle-distorted N,N’-dimethylated porphyrin isomers, an N21,N’22-dimethylated porphyrin ( anti -Me₂P ) and an N21,N’23-dimethylated porphyrin ( syn -Me₂P ) as catalysts and ferrocene derivatives as electron donors in the presence of protic acids in acetonitrile. The higher catalytic performance in an oxygen reduction reaction (ORR) was achieved by anti -Me₂P with higher turnover number (TON=250 for 30 min) than that by syn -Me₂P (TON=218 for 60 min). The reactive intermediates in the catalytic ORR were confirmed to be the corresponding isophlorins ( anti -Me₂Iph or syn -Me₂Iph ) by spectroscopic measurements. The rate-determining step in the catalytic ORRs was concluded to be proton-coupled electron-transfer reduction of O₂ with isophlorins based on kinetic analysis. The ORR rate by anti -Me₂Iph was accelerated by external protons, judging from the dependence of the observed initial rates on acid concentrations. In contrast, no acceleration of the ORR rate with syn -Me₂Iph by external protons was observed. The different mechanisms in the O₂ reduction by the two isomers should be derived from that of the arrangement of hydrogen bonding of a O₂ with inner NH protons of the isophlorins.