A trace formula for scattering resonances of unbalanced quantum graphs

2022/06/24 by Maxime Ingremeau, Ingremeau, Maxime
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Random Matrices and Applications #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2206.12460

openalex publication_date 2022/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given an unbalanced open quantum graph, we derive a formula relating sums over its scattering resonances with integrals outside a strip. We deduce lower bounds on the number of resonances (in bounded regions of the complex plane),that are independent of the size of the graph. We also deduce partial results indicating that Benjamini-Schramm convergence of open quantum graphs should imply convergence of the empirical spectral measures.

Related

• Statistical properties of resonance widths for open quantum graphs
• Equivalence of resolvent and scattering resonances on quantum graphs
• Topological Resonances on Quantum Graphs
• Non-Weyl Resonance Asymptotics for Quantum Graphs
• Empirical spectral measures of quantum graphs in the Benjamini-Schramm\n limit