Vol. 4, No. 5, 2011

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18, 1 issue

Volume 17, 10 issues

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1948-206X (online)
ISSN 2157-5045 (print)
 
Author index
To appear
 
Other MSP journals
Non-Weyl resonance asymptotics for quantum graphs

E. Brian Davies and Alexander Pushnitski

Vol. 4 (2011), No. 5, 729–756
Abstract

We consider the resonances of a quantum graph G 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 G in a disc of a large radius. We call G a Weyl graph if the coefficient in front of this leading term coincides with the volume of the compact part of G. 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
Mathematical Subject Classification 2000
Primary: 34B45
Secondary: 35B34, 47E05
Milestones
Received: 22 March 2010
Revised: 2 August 2010
Accepted: 14 September 2010
Published: 16 February 2012

Proposed: Terence Tao
Authors
E. Brian Davies
Department of Mathematics
King’s College London
Strand
London WC2R 2LS
United Kingdom
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
http://www.mth.kcl.ac.uk/staff/a_pushnitski.html