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 will in fact 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.
King’s College London campus map.