Speaker: Simon Schrader
Title: Rothe's method for time evolution in strong laser fields with Explicitly Correlated Gaussians
Abtract: Simulating the accurate time evolution of quantum mechanical systems in external fields makes it possible to analyse and investigate time-dependent phenomena such as high harmonic generation (HHG). Solving the time-dependent Schrödinger equation, however, remains challenging even for small atomic and molecular systems, and there is an interest in developing new numerical methods for the time-evolution of atoms and molecules. Recently, Kvaal et al. have proposed a new algorithm for the time evolution of small quantum mechanical systems employing Rothe's method for time propagation of Explicitly Correlated Gaussians that represent the wave function. In this method, the nonlinear basis set parameters, as well as the number of basis functions, are allowed to vary in time, producing an "optimal" basis at every time step. By adding sufficiently many basis functions, the time evolution error can be kept as small as desired. In this talk, we present the theory regarding high harmonic generation, Explicitly Correlated Gaussians and Rothe's method applied to the Hydrogen atom and show that Rothe's method is able to describe the time evolution of the Hydrogen wave function well enough to produce HHG-spectra with a quality approaching that of a grid calculation.