A Remark on Helical Waveguides (2008)
Abstract. Motivated by a proposal to create an optical helix-shaped waveguides for cold atoms and molecules, we discuss local perturbations which can create bound states in such a setting. This is...
We consider Schr\"odinger operator in dimension $d\ge 2$ with a singular interaction supported by an infinite family of concentric spheres, analogous to a system studied by Hempel and coauthors for...
A remark on helical waveguides (2007)
Motivated by a proposal to create an optical helix-shaped waveguides for cold atoms and molecules, we discuss local perturbations which can create bound states in such a setting. This is known about...
On the critical exponent in an isoperimetric inequality for chords (2007)
Exner, Pavel, Fraas, Martin, Harrell II, Evans M.
The problem of maximizing the $L^p$ norms of chords connecting points on a closed curve separated by arclength $u$ arises in electrostatic and quantum--mechanical problems. It is known that among all...
Resonance asymptotics in the generalized Winter model (2006)
We consider a modification of the Winter model describing a quantum particle in presence of a spherical barrier given by a fixed generalized point interaction. It is shown that the three classes of...
The decay law can have an irregular character (2006)
Within a well-known decay model describing a particle confined initially within a spherical $\delta$ potential shell, we consider the situation when the undecayed state has an unusual energy...