Optimal control of self-consistent classical and quantum particle systems

在这个项目中，我们将从解析和数值的角度研究自洽相互作用量子粒子系统的最优控制问题。这将涉及微观和宏观量子模型，它们有两个主要共同特征：控制以双线性方式进入偏微分方程组，在所有模型中，粒子相互作用通过自洽的静电势发生。这种特殊的模型结构出现在许多不同类型的应用中，如(量子)半导体器件、最优量子控制或生物医学应用，它可以用来构造快速的、非标准的优化算法。这个项目的主要目标是了解自洽耦合对最优控制的影响，以及量子效应和粒子相互作用的相互作用。

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.