2021/03/30 by E. Sadurní, Sadurni, Emerson, T. H. Seligman +1
Chemistry · Physics and Astronomy · #Advanced Chemical Physics Studies #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Photochemistry and Electron Transfer Studies #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2103.16727
openalex publication_date 2021/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A general treatment of the spectral problem of quantum graphs and tight-binding models in finite Hilbert spaces is given. The direct spectral problem and the inverse spectral problem are written in terms of simple algebraic equations containing information on the topology of a quantum graph. The inverse problem is shown to be combinatorial, and some low dimensional examples are explicitly solved. For a \it window graph, a commutator and anticommutator algebra (superalgebra) is identified as the culprit behind accidental degeneracy in the form of triplets, where configurational symmetry \it alone fails to explain the result. For a Möbius cycloacene graph, it is found that the accidental triplet cannot be explained with a superalgebra, but that the graph can be built unambiguously from the spectrum using combinatorial methods. These examples are compared with a more symmetric but less degenerate system, i.e. a \it car wheel graph which possesses neither triplets, nor superalgebra.