Optimal control of self-consistent classical and quantum particle systems

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In this project we will study optimal control problems for self-consistent interacting quantum particle systems from the analytical and numerical point of view. This will involve microscopic as well as macroscopic quantum models, which have two main features in common: The control enters in a bilinear manner into the partial differential equations and in all models particle interaction takes place via a self-consistent electrostatic potential. This special model structure appears in many different types of applications, like (quantum) semiconductor devics, optimal quantum control or biomedical applications and it can be used to construct fast, nonstandard optimization algorithms. The main goals of this project are to understand the influence of the self-consistent coupling on the optimal control as well as the interplay of quantum effects and particle interactions.