37 citations · 81 across the 8 of their papers we have counts for
Showing 2012Show all
3 papers · 1 filter
math.AP2012★ 3 cited
Heat trace asymptotics for quantum graphs
Ralf Rueckriemen
We consider a quantum graph where the operator contains a potential. We show that this operator admits a heat kernel. Under some assumptions on the potential, this heat kernel admi…
math-ph2012★ 10 cited
Trace Formulae for quantum graphs with edge potentials
Ralf Rueckriemen, Uzy Smilansky
This work explores the spectra of quantum graphs where the Schrödinger operator on the edges is equipped with a potential. The scattering approach, which was originally introduced…
math.SP2012★ 1 cited
Quasi-isospectrality on quantum graphs
Ralf Rueckriemen
Consider two quantum graphs with the standard Laplace operator and non-Robin type boundary conditions at all vertices. We show that if their eigenvalue-spectra agree everywhere asi…