Solving the Dirac equation on a GPU for strong-field processes in multidimensional background fields

2025/12/18 by Torgrimsson, Greger
#FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2512.16889

Abstract

In this paper, we show how to solve the Dirac equation, (iγ^μ[∂_μ+ieA_μ(t,\bf x)]-m)ψ=0, on a GPU. This is orders of magnitude faster than solving it on CPU and allows us to consider background fields, A_μ(t,\bf x), that depend on 2+1 or even 3+1 coordinates. Our approach is conveniently implemented using the computational library JAX. We show how to obtain the probabilities of Schwinger and nonlinear Breit-Wheeler pair production from these solutions using a scattered-wave-function approach and compare the results with the worldline-instanton approximations.

Citations

• JAX-in-Cell: A Differentiable Particle-in-Cell Code for Plasma Physics Applications
• Momentum correlation in pair production by spacetime dependent fields from scattered wave functions
• Schwinger pair production in spacetime fields: Moiré patterns, Aharonov-Bohm phases, and Sturm-Liouville eigenvalues
• Momentum spectrum of nonlinear Breit-Wheeler pair production in space-time fields
• Momentum spectrum of Schwinger pair production in four-dimensional e-dipole fields
• On Neural Differential Equations
• Electron-positron pair production in inhomogeneous electromagnetic fields

Cited by

• Worldline instantons for nonperturbative particle production by space and time dependent gravitational fields

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