2014/05/12 by Yulia Yu. Ershova, Ershova, Yulia, Irina I. Karpenko +3
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Quantum optics and atomic interactions #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1405.2997
openalex publication_date 2014/05/12 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
Laplacian operators on finite compact metric graphs are considered under the\nassumption that matching conditions at graph vertices are of \δ and\n\δ' types. An infinite series of trace formulae is obtained which link\ntogether two different quantum graphs under the assumption that their spectra\ncoincide. The general case of graph Schrodinger operators is also considered,\nyielding the first trace formula. Tightness of results obtained under no\nadditional restrictions on edge lengths is demonstrated by an example. Further\nexamples are scrutinized when edge lengths are assumed to be rationally\nindependent. In all but one of these impossibility of isospectral\nconfigurations is ascertained.\n