Open quantum dots: resonances from perturbed symmetry and bound states in strong magnetic fields

TL;DR

This paper investigates how symmetry-breaking perturbations, such as magnetic fields or deformations, affect resonances and bound states in open quantum dots modeled by the Noeckel system, providing perturbative and spectral analysis.

Contribution

It introduces a perturbative framework for analyzing resonance shifts due to symmetry breaking and establishes conditions for the persistence of bound states under strong magnetic fields.

Findings

Resonances emerge from embedded eigenvalues when symmetry is broken.

A perturbative expansion for resonances under weak symmetry breaking is derived.

Conditions are identified under which bound states survive 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.