The Erwin Schrr Odinger International Institute for Mathematical Physics Strong Magnetic Elds, Dirichlet Boundaries, and Spectral Gaps Strong Magnetic Elds, Dirichlet Boundaries, and Spectral Gaps

The Erwin Schrr Odinger International Institute for Mathematical Physics Rayleigh{type Isoperimetric Inequality with a Homogeneous Magnetic Field Rayleigh-type Isoperimetric Inequality with a Homogeneous Magnetic Eld

We prove that the two dimensional free magnetic Schrr odinger operator, with a xed constant magnetic eld and Dirichlet boundary conditions on a planar domain with a given area, attains its smallest possible eigenvalue if the domain is a disk. We also give some rough bounds on the lowest magnetic eigenvalue of the disk. Running title: Magnetic Rayleigh-type inequality.

Localization near Band Edges for Random Schr Odinger Operators

In this article, we prove exponential localization for wide classes of Schrr odi-nger operators, including those with magnetic elds, at the edges of unper-turbed spectral gaps. We assume that the unperturbed operator H 0 has an open gap I 0 (B ? ; B +). The random potential is assumed to be Anderson-type with independent, identically distributed coupling constants. The common density may have e...

The Erwin Schrr Odinger International Institute for Mathematical Physics Topologically Nontrivial Field Conngurations in Noncommutative Geometry Topologically Nontrivial Field Conngurations in Noncommutative Geometry 1

In the framework of noncommutative geometry we describe spinor elds with nonvanishing winding number on a truncated (fuzzy) sphere. The corresponding eld theory actions conserve all basic symmetries of the standard commutative version (space isometries and global chiral symmetry), but due to the noncommutativity of the space the elds are regularized and they contain only nite number of modes. 2...

Institute for Mathematical Physics Existence and Semi{classical Limit of the Least Energy Solution to a Nonlinear Schrr Odinger Equation with Electromagnetic Fields Existence and Semi-classical Limit of the Least Energy Solution to a Nonlinear Schrr Odinger Equation with Electromagnetic Elds

On Eigenvalues in Gaps for Perturbed Magnetic Schrr Odinger Operators

1 Introduction (1) We consider Schrr odinger operators with a spectral gap, perturbed by either a decreasing electric potential or a decreasing magnetic eld. The strength of these perturbations depends on a coupling parameter. With growing, eigenvalues may move into the gap or out of the gap. Most of our results concern (lower) bounds for the number of eigenvalues that cross a xed energy level ...