Pseudospectral methods for atoms in strong magnetic fields

TL;DR

This paper introduces a simple and fast pseudospectral algorithm for calculating atomic structures in strong magnetic fields, achieving high accuracy and outperforming existing methods in speed.

Contribution

The authors develop a new pseudospectral method that is simpler and significantly faster than finite-element approaches for atoms in strong magnetic fields.

Findings

Achieves better than 1% accuracy for atoms in zero magnetic field.

Matches state-of-the-art results for hydrogen, helium, and lithium in strong magnetic fields.

Algorithm is approximately 100 to 100,000 times faster than finite-element methods.

Abstract

We present a new pseudospectral algorithm for the calculation of the structure of atoms in strong magnetic fields. We have verified this technique for one, two and three-electron atoms in zero magnetic fields against laboratory results and find typically better than one-percent accuracy. We further verify this technique against the state-of-the-art calculations of hydrogen, helium and lithium in strong magnetic fields (up to about $2\times 10^{6}$ T) and find a similar level of agreement. The key enabling advantages of the algorithm are its simplicity (about 130 lines of commented code) and its speed (about $10^2-10^5$ times faster than finite-element methods to achieve similar accuracy).