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Non-Weyl resonance asymptotics for quantum graphs in a magnetic field |
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| Authors: | Pavel Exner Ji?í Lipovský |
| Institution: | a Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University, B?ehová 7, 11519 Prague, Czech Republic b Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 ?e? near Prague, Czech Republic c Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University, V Holešovi?kách 2, 18000 Prague, Czech Republic |
| 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. |
| Keywords: | Quantum graphs Magnetic field Resonances Weyl asymptotics |
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