Relativistic Real-Time Methods

TL;DR

This paper reviews relativistic real-time electronic structure methods, focusing on their theoretical foundations, computational techniques, and applications in ultrafast spectroscopy involving non-linear light-matter interactions.

Contribution

It provides a comprehensive overview of relativistic real-time electron dynamics methods, including theoretical formulations, Hamiltonians, and numerical techniques, with emphasis on modern two-component approaches.

Findings

Summarizes the relativistic Hamiltonian and equations of motion for electron dynamics.

Discusses various numerical propagation and signal processing techniques.

Highlights applications in frequency- and time-resolved spectroscopies.

Abstract

Recent advances in laser technology enable to follow electronic motion at its natural time-scale with ultrafast pulses, leading the way towards atto- and femtosecond spectroscopic experiments of unprecedented resolution. Understanding of these laser-driven processes, which almost inevitably involve non-linear light-matter interactions and non-equilibrium electron dynamics, is challenging and requires a common effort of theory and experiment. Real-time electronic structure methods provide the most straightforward way to simulate experiments and to gain insights into non-equilibrium electronic processes. In this Chapter, we summarize the fundamental theory underlying the relativistic particle-field interaction Hamiltonian as well as equation-of-motion for exact-state wave function in terms of the one- and two-electron reduced density matrix. Further, we discuss the relativistic real-time electron dynamics mean-field methods with an emphasis on Density-Functional Theory and Gaussian basis, starting from the four-component (Dirac) picture and continue to the two-component (Pauli) picture, where we introduce various flavours of modern exact two-component (X2C) Hamiltonians for real-time electron dynamics. We also overview several numerical techniques for real-time propagation and signal processing in quantum electron dynamics. We close this Chapter by listing selected applications of real-time electron dynamics to frequency-resolved and time-resolved spectroscopies.