Enhanced classical radiation damping of electronic cyclotron motion in the vicinity of the Van Hove singularity in a waveguide

TL;DR

This paper investigates how Van Hove singularities in waveguides significantly enhance classical radiation damping of electron cyclotron motion, leading to faster decay and observable non-Markovian effects without runaway solutions.

Contribution

It introduces a non-perturbative classical model showing enhanced damping near Van Hove singularities, avoiding traditional runaway issues.

Findings

Decay process is amplified (~10^4) near the Van Hove singularity.

Branch-point effects are also significantly enhanced.

Decay timescales are dramatically shortened.

Abstract

We study the damping process of electron cyclotron motion and the resulting emission in a waveguide using the classical Friedrichs model without relying on perturbation analysis such as Fermi's golden rule. A classical Van Hove singularity appears at the lower bound (or cut-off frequency) of the dispersion associated with each of the electromagnetic field modes in the waveguide. In the vicinity of the Van Hove singularity, we found that not only is the decay process associated with the resonance pole enhanced (amplification factor ~ $10^4$) but the branch-point effect is also comparably enhanced. As a result, the timescale on which most of the decay occurs is dramatically shortened. Further, this suggests that the non-Markovian branch point effect should be experimentally observable in the vicinity of the Van Hove singularity. Our treatment yields a physically-acceptable solution without the problematic runaway solution that is well known to appear in the traditional treatment of classical radiation damping based on the Abraham-Lorentz equation.