A Fermi golden rule for quantum graphs

Abstract

We present a Fermi golden rule giving rates of decay of states obtained by perturbing embedded eigenvalues of a quantum graph. To illustrate the procedure in a notationally simpler setting we also present a Fermi Golden Rule for boundary value problems on surfaces with constant curvature cusps. We also provide a resonance existence result which is uniform on compact sets of energies and metric graphs. The results are illustrated by numerical experiments.

21 pages, 4 figures

References in corpus (1)

• Metastable states when the Fermi Golden Rule constant vanishes

Cited by in corpus (6)

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• Spectrum of a non-selfadjoint quantum star graph
• Pseudo-orbit approach to trajectories of resonances in quantum graphs with general vertex coupling: Fermi rule and high-energy asymptotics
• Application of topological resonances in experimental investigation of a Fermi golden rule in microwave networks
• On the multilevel internal structure of the asymptotic distribution of resonances
• Scattering resonances of large weakly open quantum graphs