Non-Weyl resonance asymptotics for quantum graphs in a magnetic field

0366262 - ÚJF 2012 RIV NL eng J - Journal Article
Exner, Pavel - Lipovský, J.
Non-Weyl resonance asymptotics for quantum graphs in a magnetic field.
Physics Letters. A. Roč. 375, č. 4 (2011), s. 805-807. ISSN 0375-9601. E-ISSN 1873-2429
R&D Projects: GA MŠMT LC06002; GA ČR GAP203/11/0701
Institutional research plan: CEZ:AV0Z10480505
Keywords : Quantum graphs * Magnetic field * Resonances
Subject RIV: BG - Nuclear, Atomic and Molecular Physics, Colliders
Impact factor: 1.632, year: 2011

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. (C) 2010 Elsevier B.V. All rights reserved.
Permanent Link: http://hdl.handle.net/11104/0201315