Classical Radiation Damping and Fano Interference in Cyclotron Motion based on Liouvillian Complex Eigenvalue Problem

We study the emission of light due to classical radiation damping of an electron that undergoes cyclotron motion inside an electromagnetic waveguide by solving the Liouville equation. A classical Van Hove singularity appears at the lower bound of each continuum mode (i.e., at each cut-off frequency) that supports light transport in the waveguide. Based on the complex spectral representation of the Liouvillian in terms of classical coherent states, we found a similar structure to the quantum Fano spectrum and Fano gap in the light spectrum in the vicinity of the classical Van Hove singularity.