Locally Perturbed Random Walks with Unbounded Jumps

In \cite{SzT}, D. Sz\'asz and A. Telcs have shown that for the diffusively scaled, simple symmetric random walk, weak convergence to the Brownian motion holds even in the case of local impurities if $d \ge 2$. The extension of their result to finite range random walks is straightforward. Here, however, we are interested in the situation when the random walk has unbounded range. Concretely we generalize the statement of \cite{SzT} to unbounded random walks whose jump distribution belongs to the domain of attraction of the normal law. We do this first: for diffusively scaled random walks on $\mathbf Z^d$ $(d \ge 2)$ having finite variance; and second: for random walks with distribution belonging to the non-normal domain of attraction of the normal law. This result can be applied to random walks with tail behavior analogous to that of the infinite horizon Lorentz-process; these, in particular, have infinite variance, and convergence to Brownian motion holds with the superdiffusive $\sqrt{n \log n}$ scaling.Comment: 16 page

On the changes of the electronic structure of early-transition-metal-systems at hydrogenation

The hydrogenation effect on Sc, Y, La, Cd and Eu has been investigated by XPS. The stability, the charge transfer as well as the microscopic behaviours of the processes have been discussed

CLOSE-PACKED FRANK-KASPER COORDINATION AND HIGH CRITICAL TEMPERATURE SUPERCONDUCTIVITY

It has been proposed that a relation exists between close packed Frank-Kasper co-ordination in the layers containing Cu-O planes and high-Tc superconductivity. The origin of the superconductivity in perovskite-type materials is attributed in part to a three dimensional nesting of the Fermi-surface with the boundary of Jones-zone, causing 'partially-gapped' Fermi surface and to a gliding charge density wave arising from a three-dimensional 'breathing' of distorted perovskite structures associated with close-packed seeking symmetry

On the protection of the isolation at the fabrication of all niobium josepshson-junctions

The protection mechanism of thin gold layer for preparation of all-niobium devices is discussed. A suggestion on the electronic origin of protection is presented

Characterization of the nitrogen split interstitial defect in wurtzite aluminum nitride using density functional theory

We carried out Heyd-Scuseria-Ernzerhof hybrid density functional theory plane wave supercell calculations in wurtzite aluminum nitride in order to characterize the geometry, formation energies, transition levels and hyperfine tensors of the nitrogen split interstitial defect. The calculated hyperfine tensors may provide useful fingerprint of this defect for electron paramagnetic resonance measurement.Comment: 5 pages, 3 figure

Theoretical model of the dynamic spin polarization of nuclei coupled to paramagnetic point defects in diamond and silicon carbide

Dynamic nuclear spin polarization (DNP) mediated by paramagnetic point defects in semiconductors is a key resource for both initializing nuclear quantum memories and producing nuclear hyperpolarization. DNP is therefore an important process in the field of quantum-information processing, sensitivity-enhanced nuclear magnetic resonance, and nuclear-spin-based spintronics. DNP based on optical pumping of point defects has been demonstrated by using the electron spin of nitrogen-vacancy (NV) center in diamond, and more recently, by using divacancy and related defect spins in hexagonal silicon carbide (SiC). Here, we describe a general model for these optical DNP processes that allows the effects of many microscopic processes to be integrated. Applying this theory, we gain a deeper insight into dynamic nuclear spin polarization and the physics of diamond and SiC defects. Our results are in good agreement with experimental observations and provide a detailed and unified understanding. In particular, our findings show that the defects' electron spin coherence times and excited state lifetimes are crucial factors in the entire DNP process