Open quantum dots: resonances from perturbed symmetry and bound states in strong magnetic fields
Abstract
We discuss the Noeckel model of an open quantum dot, i.e., a straight hard-wall channel with a potential well. If this potential depends on the longitudinal variable only, there are embedded eigenvalues which turn into resonances if the symmetry is violated, either by applying a magnetic field or by deformation of the well. For a weak symmetry breaking we derive the perturbative expansion of these resonances. We also deduce a sufficient condition under which the discrete spectrum of such a system (without any symmetry) survives the presence of a strong magnetic field. It is satisfied, in particular, if the dot potential is purely attractive.
Keywords
Cite
@article{arxiv.math-ph/0006031,
title = {Open quantum dots: resonances from perturbed symmetry and bound states in strong magnetic fields},
author = {Pierre Duclos and Pavel Exner and Bernhard Meller},
journal= {arXiv preprint arXiv:math-ph/0006031},
year = {2020}
}
Comments
LaTeX, 15 pages; a revised text to appear in Rep. Math. Phys.; a changed title plus a few minor corrections