Appears in collection : Evolution equations on singular spaces / Équations d'évolution sur les espaces singuliers
We prove a quantum Sabine law for the location of resonances in transmission problems. In this talk, our main applications are to scattering by strictly convex, smooth, transparent obstacles and highly frequency dependent delta potentials. In each case, we give a sharp characterization of the resonance free regions in terms of dynamical quantities. In particular, we relate the imaginary part of resonances to the chord lengths and reflectivity coefficients for the ray dynamics and hence give a quantum version of the Sabine law from acoustics.
By Dean Baskin
By Irina Mitrea
