Heat trace asymptotics for quantum graphs
Analysis of PDEs
2012-12-13 v1
Abstract
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 admits an asymptotic expansion at t=0 with coefficients that depend on the potential in a universal way. These coefficients are spectral invariants, we compute the first few of them.
Cite
@article{arxiv.1212.2840,
title = {Heat trace asymptotics for quantum graphs},
author = {Ralf Rueckriemen},
journal= {arXiv preprint arXiv:1212.2840},
year = {2012}
}