Open quantum dots: resonances from perturbed symmetry and bound states in 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.

LaTeX, 15 pages; a revised text to appear in Rep. Math. Phys.; a changed title plus a few minor corrections

References in corpus (1)

• Bound states and transmission antiresonances in parabolically confined cross structures: influence of weak magnetic fields

Cited by in corpus (9)

• Controlling Directionality and Dimensionality of Wave Propagation through Separable Bound States in the Continuum
• Convergence of resonances on thin branched quantum wave guides
• Properties of trapped electromagnetic modes in coupled waveguides
• Resonances in twisted quantum waveguides
• Resonances in Models of Spin Dependent Point Interactions
• Perturbations of eigenvalues embedded at threshold: one, two and three dimensional solvable models
• Suppressing deleterious effects of spontaneous emission in creating bound states in cold atom continuum
• Coupled system of Dirac fermions with different Fermi velocities via composites of SUSY operators
• A quantum waveguide with Aharonov Bohm magnetic field