More ergodic billiards with an infinite cusp

In a previous paper (nlin.CD/0107041) the following class of billiards was studied: For $f: [0, +\infty) \longrightarrow (0, +\infty)$ convex, sufficiently smooth, and vanishing at infinity, let the billiard table be defined by $Q$, the planar domain delimited by the positive $x$-semiaxis, the positive $y$-semiaxis, and the graph of $f$. For a large class of $f$ we proved that the billiard map was hyperbolic. Furthermore we gave an example of a family of $f$ that makes this map ergodic. Here we extend the latter result to a much wider class of functions.Comment: 13 pages, 4 figure

Localization in a strongly disordered system: A perturbation approach

We prove that a strongly disordered two-dimensional system localizes with a localization length given analytically. We get a scaling law with a critical exponent is $\nu=1$ in agreement with the Chayes criterion $\nu\ge 1$. The case we are considering is for off-diagonal disorder. The method we use is a perturbation approach holding in the limit of an infinitely large perturbation as recently devised and the Anderson model is considered with a Gaussian distribution of disorder. The localization length diverges when energy goes to zero with a scaling law in agreement to numerical and theoretical expectations.Comment: 5 pages, no figures. Version accepted for publication on International Journal of Modern Physics

Introduction to Library Trends 23 (3) Winter 1975: Music and Fine Arts in the General Library

published or submitted for publicatio

Electron density distribution and screening in rippled graphene sheets

Single-layer graphene sheets are typically characterized by long-wavelength corrugations (ripples) which can be shown to be at the origin of rather strong potentials with both scalar and vector components. We present an extensive microscopic study, based on a self-consistent Kohn-Sham-Dirac density-functional method, of the carrier density distribution in the presence of these ripple-induced external fields. We find that spatial density fluctuations are essentially controlled by the scalar component, especially in nearly-neutral graphene sheets, and that in-plane atomic displacements are as important as out-of-plane ones. The latter fact is at the origin of a complicated spatial distribution of electron-hole puddles which has no evident correlation with the out-of-plane topographic corrugations. In the range of parameters we have explored, exchange and correlation contributions to the Kohn-Sham potential seem to play a minor role.Comment: 13 pages, 13 figures, submitted. High-quality figures can be requested to the author