Understanding Radiation Reaction via Structure-Preserving Algorithms for Coupled Schrödinger-Maxwell Systems

Classically, a charged particle in a magnetic field emits radiation, losing momentum and experiencing the Abraham–Lorentz (AL) radiation reaction (RR) force. At atomic scales, however, the assumptions behind the AL equation fail, and theory indicates that RR destroys the coherent state of an electron—undermining the very concept of a RR force. This process can be described by the coupled Schrödinger–Maxwell (SM) system, but the system’s nonlinear complexity has long limited its use for probing the quantum-to-classical transition. We present geometric structure-preserving algorithms for the SM system that preserve gauge invariance, symplecticity, and unitarity on the discrete space-time lattice, which are implemented in our Structure-Preserving scHrödINger maXwell (SPHINX) code. By constructing coherent states from the Landau levels, SPHINX simulates the fully coupled nonlinear dynamics of an electron coherent state, the energy partition evolution, and decoherence/relaxation of the electron wave packet in time due to RR. This opens a new computational window for RR physics and advances modeling of extreme-field phenomena in fusion plasmas, astrophysics, and next-generation laser experiments.



Supported by the U.S. DOE (DE-AC02-09CH11466) and NSF GRFP (KB0013612).