  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.
