Solving the Dirac equation on a GPU for strong-field processes in multidimensional background fields
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918255435710464 |
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| author | Torgrimsson, Greger |
| author_facet | Torgrimsson, Greger |
| contents | In this paper, we show how to solve the Dirac equation, $(iγ^μ[\partial_μ+ieA_μ(t,{\bf x})]-m)ψ=0$, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_16889 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solving the Dirac equation on a GPU for strong-field processes in multidimensional background fields Torgrimsson, Greger High Energy Physics - Phenomenology High Energy Physics - Theory In this paper, we show how to solve the Dirac equation, $(iγ^μ[\partial_μ+ieA_μ(t,{\bf x})]-m)ψ=0$, 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. |
| title | Solving the Dirac equation on a GPU for strong-field processes in multidimensional background fields |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.16889 |