Computational relativistic quantum dynamics and its application to relativistic tunneling and Kapitza-Dirac scattering

TL;DR

This paper develops numerical methods for solving relativistic quantum equations, enabling the simulation of phenomena like tunneling in strong laser fields and relativistic Kapitza-Dirac scattering, which are difficult to analyze analytically.

Contribution

It introduces GPU-accelerated computational techniques for solving the Dirac and Klein-Gordon equations in relativistic quantum dynamics.

Findings

Simulation of tunneling from highly charged ions in strong laser fields

Analysis of relativistic Kapitza-Dirac scattering phenomena

Demonstration of high-performance computational implementation

Abstract

Computational methods are indispensable to study the quantum dynamics of relativistic light-matter interactions in parameter regimes where analytical methods become inapplicable. We present numerical methods for solving the time-dependent Dirac equation and the time-dependent Klein-Gordon equation and their implementation on high performance graphics cards. These methods allow us to study tunneling from hydrogen-like highly charged ions in strong laser fields and Kapitza-Dirac scattering in the relativistic regime.