Equivalence of resolvent and scattering resonances on quantum graphs

2006/10/25 by Exner, Pavel, Lipovský, Jiří
#81V99 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Physics (quant-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.math-ph/0610065

Abstract

We discuss resonances for Schrödinger 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 δ-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.

Related

• Topological Resonances on Quantum Graphs
• A trace formula for scattering resonances of unbalanced quantum graphs
• Statistical properties of resonance widths for open quantum graphs
• Resolvent expansion for the Schrödinger operator on a graph with infinite rays
• Spectral Theory for Schrödinger operators on compact metric graphs with δ and δ' couplings: a survey