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arXiv · 2512.16889

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

Greger Torgrimsson
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Abstract

In this paper, we show how to solve the Dirac equation, $(i\gamma^\mu[\partial_\mu+ieA_\mu(t,{\bf x})]-m)\psi=0$, on a GPU. This is orders of magnitude faster than solving it on CPU and allows us to consider background fields, $A_\mu(t,{\bf x})$, 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.

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Greger Torgrimsson. 2025-12-18. Solving the Dirac equation on a GPU for strong-field processes in multidimensional background fields. https://arxiv.org/abs/2512.16889

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