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

We discuss the Nِckel 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.