Classical Tunneling from the Lorentz-Dirac Equation

TL;DR

This paper introduces a novel class of solutions to the Lorentz-Dirac equation that describe classical tunneling phenomena, providing explicit solutions for nonrelativistic electrons and exploring their persistence across different potentials.

Contribution

It presents the first classical tunneling solutions within the Lorentz-Dirac framework, expanding understanding of radiation reaction effects in classical charged particle dynamics.

Findings

Explicit solutions for nonrelativistic electron tunneling over square barriers

Persistence of tunneling solutions for smoother potentials

Initial conditions can lead to discrete ambiguities in particle trajectories

Abstract

The classical equation of motion of a charged point particle, including its radiation reaction, is described by the Lorentz-Dirac equation. We found a new class of solutions that describe tunneling (in a completely classical context!). For nonrelativistic electrons and a square barrier, the solution is elementary and explicit. We show the persistance of the solution for smoother potentials. For a large range of initial velocities, initial conditions may leave a (discrete) ambiguity on the resulting motion.