Pierre Duclos, Pavel Exner, Bernhard Meller
Resonances from perturbed symmetry in open quantum dots
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ABSTRACT. We discuss the N\"ockel 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.