50,718 research outputs found
More ergodic billiards with an infinite cusp
In a previous paper (nlin.CD/0107041) the following class of billiards was
studied: For convex,
sufficiently smooth, and vanishing at infinity, let the billiard table be
defined by , the planar domain delimited by the positive -semiaxis, the
positive -semiaxis, and the graph of .
For a large class of we proved that the billiard map was hyperbolic.
Furthermore we gave an example of a family of 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 in agreement with the Chayes criterion . 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
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