10-190 Pavel Exner, Jiri Lipovsky

Non-Weyl resonance asymptotics for quantum graphs in a magnetic field (104K, pdf) Nov 26, 10

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Abstract. We study asymptotical behaviour of resonances for a quantum graph consisting of a finite internal part and external leads placed into a magnetic field, in particular, the question whether their number follows the Weyl law. We prove that the presence of a magnetic field cannot change a non-Weyl asymptotics into a Weyl one and vice versa. On the other hand, we present examples demonstrating that for some non-Weyl graphs the ``effective size'' of the graph, and therefore the resonance asymptotics, can be affected by the magnetic field.

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