Time Evolution for Quantum Dynamics with Efficient Solvers

 

 

 

 

 

Time Evolution for Quantum Dynamics with Efficient Solvers

Supervisors: Prof. Daniela Pfannkuche (UHH), Dr. Sebastian Götschel (TUHH), Prof. Daniel Ruprecht (TUHH)

Watching the “molecular movie” in real time still needs an interpreter: a quantum chemical calculation which translates measured signals into the correlated dance of electrons and nuclei. Accurate computational modelling of the quantum dynamics of many-body systems, however, is still a very challenging problem. Long-time stability, accuracy and, in particular, excessive solution times are all issues that are still not fully solved.
Building on modern methods from numerical analysis, the project aims to improve the accuracy and performance of simulations by developing new tailored numerical time stepping algorithms for the Schrödinger equation, which underlies simulations of quantum dynamics. The development will focus in particular on the use of geometric time stepping methods in combination with rational Krylov methods for the fast and accurate solution of linear systems of differential equations.

Apply here!