Equivalence of resolvent and scattering resonances on quantum graphs

Details Equivalence of resolvent and scattering resonances on quantum graphs Equivalence of resolvent and scattering resonances on quantum graphs

2006-10-25

arxiv.org/abs/math-ph/0610065v1

Physics

Mathematical Physics

9 pages, AMS-LaTeX, written for proceedings of a conference in honour of J.-M. Combes, Cergy-Pontoise, September 2006

Scientific paper

We discuss resonances for Schr\"odinger operators on metric graphs which
consists of a finite compact part and a finite number of halflines attached to
it; the vertex coupling is assumed to be of the $\delta$-type or certain
modifications of it. Using exterior complex scaling on the graph we show that
the resolvent and scattering resonances coincide in this case.

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