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

Pierre Duclos·Pavel Exner·Bernhard Meller
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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.

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Pierre Duclos, Pavel Exner, Bernhard Meller. 2000-06-29. Open quantum dots: resonances from perturbed symmetry and bound states in strong magnetic fields. https://doi.org/10.1016/s0034-4877(01)80041-0

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