Comparative study of the performance of various time propagators to solve the time-dependent Schrödinger equation

A. L. FRAPICCINI, S.SCHRÖTER, B. PIRAUX, A. HAMIDO, J. MADROÑERO, P. OMAHONY, F. MOTA- FURTADO, J. EIGLSPERGER

Cluj-Napoca

Encuentro; 4th annual meeting of the COST Action CUSPFEL; 2012

We present a comparison between different time-propagation schemes in the case where high accuracy is required (about 10 digits precision in the conservation of the norm). One of the propagators is based on a predictor-corrector scheme with an explicit method as the predictor. Automatic adjustment of the time step and accuracy control as a function of some tolerance are the important keys of this method. We also studied a Krylov subspace technique, which works for a fixed time step. This last scheme was also tested as a predictor in the predictor-corrector propagator, to control the variation of the time-step. The different methodologies where tested for a simple one-dimensional of a model atom in a Gaussian potential with an intense low-frequency field. The main purpose of this calculation is to gain knowledge of the behavior of the error and computation demands of each method, to develop a fully portable computer code to propagate any given time-dependent hamiltonian.