2023/07/20 by Kai‐Uwe Bux, Bux, Kai-Uwe, Joachim Hilgert +3
Mathematics · Physics and Astronomy · #05C81 #37E25 #47A11 #47B93 #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2307.10876
openalex publication_date 2023/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We compare the spectral properties of two kinds of linear operators characterizing the (classical) geodesic flow and its quantization on connected locally finite graphs without dead ends. The first kind are transfer operators acting on vector spaces associated with the set of non backtracking paths in the graphs. The second kind of operators are averaging operators acting on vector spaces associated with the space of vertices of the graph. The choice of vector spaces reflects regularity properties. Our main results are correspondences between classical and quantum spectral objects as well as some automatic regularity properties for eigenfunctions of transfer operators.