Simulation of the hydrogen ground state in Stochastic Electrodynamics

TL;DR

This paper investigates the hydrogen ground state using classical stochastic electrodynamics by numerically simulating the Abraham-Lorentz equation, extending previous work to three dimensions and longer times, but still observing ionization.

Contribution

It advances the simulation of hydrogen in stochastic electrodynamics by treating the full 3D problem and employing longer simulation times than prior studies.

Findings

Short-term results show a trend towards the ground state conjecture.

Long-term simulations indicate the atom ionizes, challenging the stability of the ground state.

The approach improves numerical modeling of the classical hydrogen atom.

Abstract

Stochastic electrodynamics is a classical theory which assumes that the physical vacuum consists of classical stochastic fields with average energy $\frac{1}{2}\hbar \omega$ in each mode, i.e., the zero-point Planck spectrum. While this classical theory explains many quantum phenomena related to harmonic oscillator problems, hard results on nonlinear systems are still lacking. In this work the hydrogen ground state is studied by numerically solving the Abraham -- Lorentz equation in the dipole approximation. First the stochastic Gaussian field is represented by a sum over Gaussian frequency components, next the dynamics is solved numerically using OpenCL. The approach improves on work by Cole and Zou 2003 by treating the full $3d$ problem and reaching longer simulation times. The results are compared with a conjecture for the ground state phase space density. Though short time results suggest a trend towards confirmation, in all attempted modelings the atom ionises at longer times.