Program

Background

Photocatalysis is a key application in the field of femtochemistry where chemical reaction dynamics is controlled by temporally shaped femtosecond laser pulses, with the target to promote specific product channels while suppressing competing undesired channels, e.g. pollutants. For catalytic systems, optimal shaping of laser pulses requires the iterated integration of the dissipative Liouville-von Neumann (LvN) equation for reduced quantum mechanical density matrices, which represents the computational bottleneck for theoretical modelling, as the size of the matrices grows quadratically with the number of quantum states involved. The aim of this project is to study model order reduction (MOR) and optimal control (OC) of LvN-based models to beat the curse of dimensionality in the simulation and control of photocatalytic processes.

Goals

    • Extending existing approaches to MOR from the linear to the bilinear case (required for LvN-based models)
    • Developing, implementing and testing numerical methods for the solution of large-scale generalized Sylvester and Lyapunov equations
    • Exploring structure preservation of MOR approaches
    • Applying MOR approaches with optimal control of open quantum systems
    • Identifying relevant photochemical benchmark systems to test various MOR / OC approaches