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

TL;DR

This paper presents a GPU-based method for efficiently solving the Dirac equation in complex, multidimensional background fields, enabling advanced simulations of strong-field quantum processes with significant speed improvements.

Contribution

The authors introduce a GPU-accelerated approach using JAX to solve the Dirac equation in higher-dimensional fields, surpassing previous CPU-based methods in speed and complexity handling.

Findings

GPU implementation is orders of magnitude faster than CPU

Able to handle 2+1 and 3+1 dimensional background fields

Results agree with worldline-instanton approximations

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.