Numerical Simulations of the Nonlinear Quantum Vacuum in the Heisenberg-Euler Weak-Field Expansion

TL;DR

This paper introduces a highly accurate numerical method for simulating nonlinear quantum vacuum effects predicted by the Heisenberg-Euler theory, enabling detailed analysis of phenomena like vacuum birefringence and harmonic generation in high-intensity laser fields.

Contribution

The paper presents a novel numerical scheme with an almost linear dispersion relation and nonphysical mode filtering for solving Heisenberg-Euler nonlinear equations in multiple dimensions.

Findings

Validated against analytical results for vacuum birefringence

Successfully simulated harmonic generation in 2D and 3D scenarios

Demonstrated the scheme's accuracy and efficiency in complex simulations

Abstract

The Heisenberg-Euler theory of the quantum vacuum supplements Maxwell's theory of electromagnetism with nonlinear light-light interactions. These originate in vacuum fluctuations, a key prediction of quantum theory, and can be triggered by high-intensity laser pulses, causing a variety of intriguing phenomena. A highly accurate numerical scheme for solving the nonlinear equations due to the leading orders of the Heisenberg-Euler weak-field expansion is presented. The algorithm possesses an almost linear vacuum dispersion relation even for comparably small wavelengths and incorporates a nonphysical modes filter. The implemented solver is tested in one spatial dimension against a set of known analytical results for vacuum birefringence and harmonic generation. More complex scenarios for harmonic generation are demonstrated in two and three spatial dimensions.