Resonance scattering at third-order exceptional points

We analyze scattering cross sections at and near third-order exceptional points (EP3), i.e., points in physical parameter space where three energies and eigenfunctions coincide. At an EP3, the Green's function contains a pole of third order, in addition to poles of second and first order. We show that the interference of the three pole terms produces a rich variety of line shapes at the exceptional point and in its neighbourhood. This is demonstrated by extending previous work on two harmonic oscillators to a system of three driven coupled damped oscillators. We also discuss the similarities and the differences in the behaviour of the amplitudes in the classical problem and the scattering cross sections in the quantum mechanical problem at the EP3.