The aim of the project MA14-002 'Adaptive Time-Splitting for Many-Body Quantum Propagation' supported by the Vienna Science and Technology Fund (WWTF) is to understand non-equilibrium quantum many-body systems, which is one of the grand challenges in current physics. The ability to describe time-dependent extended systems on a quantitative level promises to open up new technological developments such as laser control of chemical reactions, femtosecond lightfield electronics, and material design for sustainable energy. Most experimental probes of quantum many-body systems rely on so-called pump-probe schemes. The system is driven out of equilibrium and the ensuing dynamics is studied. While for weak pump and probe fields the dynamics can be understood within linear response theory where essentially equilibrium (or near ground state) properties enter, stronger pumping requires a full time-dependent propagation beyond the perturbative limit. While the high-dimensional many-particle Schrödinger equation is too complex to be solved for more than a few particles in three dimensions, practically all approximations to it give rise to coupled nonlinear partial differential equations in space and time in reduced dimensions. Still, propagation of these equations constitutes a major challenge. In this project we aim for the development and implementation of a highly efficient and accurate method, the adaptive time-splitting method, for the propagation of quantum many-body systems presently out of reach. We will investigate the efficiency, error, and speed up of this method and apply it to both fermionic and bosonic systems of current interest. So far, the project yielded the following articles and preprints and conference presentations. A collection of splitting methods constructed in the course of the project or taken from the literature and assessed as to their merits for computational purposes can be found at

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page written by Othmar Koch.
last modification: Sun Jan 28 18:00 MET 2018