Surgery transformations and eigenvalue estimates for quantum graphs with δ' vertex interactions

2022/01/31 by Aftab Ali, Muhammad Usman, Ali, Aftab +1
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Computer science #Discrete mathematics #Eigenvalues and eigenvectors #FOS: Physical sciences #Graph #Interlacing #Laplace operator #Laplacian matrix #Mathematical Physics (math-ph) #Mathematical analysis #Mathematics #Matrix Theory and Algorithms #Monotonic function #Physics #Quantum #Quantum chaos and dynamical systems #Quantum graph #Quantum mechanics #Spectral Theory in Mathematical Physics #Vertex (graph theory) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.2201.13017

arxiv created 2022/01/31 · openalex publication_date 2022/01/31 · arxiv updated 2022/02/01 · openalex created_date 2022/04/03 · openalex updated_date 2026/08/05

Abstract

We extend the surgical tool box for quantum graphs to anti-standard and δ' vertex conditions. Monotonicity properties of eigenvalues of graph Laplacian with δ' interactions at vertices depend on the sign of vertex parameter. Using several interlacing inequalities between eigenvalues of graph Laplacian with different vertex conditions and surgery principles we obtain new upper and lower bounds on the eigenvalues of δ and δ' Laplacians.

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