Very accurate time propagation of coupled Schr\"odinger equations for femto- and attosecond physics and chemistry, with C++ source code

TL;DR

This paper introduces a fast, high-precision C++ implementation of a semi-global time propagation algorithm for coupled Schrödinger equations, enabling accurate simulations of femto- and attosecond laser-matter interactions.

Contribution

The paper presents a novel, efficient C++ implementation of a semi-global propagation algorithm that achieves higher accuracy and speed than existing methods for coupled Schrödinger equations.

Findings

Achieves up to 33 decimal places precision.

Faster and more accurate than global Chebyshev propagator.

Demonstrated with five sample simulations.

Abstract

In this article, I present a very fast and high-precision (up to 33 decimal places) C++ implementation of the semi-global time propagation algorithm for a system of coupled Schr\"odinger equations with a time-dependent Hamiltonian. It can be used to describe time-dependent processes in molecular systems after excitation by femto- and attosecond laser pulses. It also works with an arbitrary user supplied Hamiltonian and can be used for nonlinear problems. The semi-global algorithm is briefly presented, the C++ implementation is described and five sample simulations are shown. The accompanying C++ source code package is included. The high precision benchmark (long double and float128) shows the estimated calculation costs. The presented method turns out to be faster and more accurate than the global Chebyshev propagator.