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Non-Weyl resonance
asymptotics for quantum graphs
E. Brian Davies and Alexander Pushnitski |
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Vol. 4 (2011), No. 5, 729–756
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Abstract |
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We consider the resonances of a quantum graph that consists of a compact part with one or more infinite leads attached to it. We discuss the leading term of the asymptotics of the number of resonances of in a disc of a large radius. We call a Weyl graph if the coefficient in front of this leading term coincides with the volume of the compact part of . We give an explicit topological criterion for a graph to be Weyl. In the final section we analyze a particular example in some detail to explain how the transition from the Weyl to the non-Weyl case occurs. |
Keywords
quantum graph, resonance, Weyl asymptotics
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Mathematical Subject Classification 2000
Primary: 34B45
Secondary: 35B34, 47E05
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Milestones
Received: 22 March 2010
Revised: 2 August 2010
Accepted: 14 September 2010
Published: 16 February 2012
Proposed: Terence Tao
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Authors |
| E. Brian Davies | |
| Department of Mathematics King’s College London Strand London WC2R 2LS United Kingdom |
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| http://www.kcl.ac.uk/nms/depts/mathematics/people/atoz/daviesb.aspx | |
| Alexander Pushnitski | |
| Department of Mathematics King’s College London Strand London WC2R 2LS United Kingdom |
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| http://www.mth.kcl.ac.uk/staff/a_pushnitski.html | |
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