Fundamental mechanisms and obstacles in the bilinear control of Schrödinger equations

量子工程是一门新兴学科，具有从根本上(重新)塑造我们的技术和经济宇宙的潜力。 它涉及受量子力学定律支配的物理系统的受控操纵。它的应用范围从精密测量设备，到密码系统，再到标志性的量子计算机。对量子系统及其控制的扎实掌握将很快成为工程师标准武器库的一部分。这项研究计划旨在确定量子控制的一些基本数学原理，以帮助发展对受控量子系统的强大直觉。将研究的现象包括色散在控制过程中的作用和量子动力学的半经典近似。由于观察到我们关于量子系统的直觉相当一部分是从几个可以明确处理的简单教科书系统中衍生出来的，因此我们将把重点放在简单 一维系统，如无限长方势垒和谐振子。

Quantum engineering is an emerging discipline with the potential of fundamentally (re-)shaping our technological and economic universes. It deals with the controlled manipulation of physical systems which are governed by the laws quantum mechanics. Its applications range from precision measurement devices, over crypto systems, to the iconic quantum computer. A solid grasp of quantum systems and their control will soon be part of the standard arsenal of engineers. This research program aims to identify some fundamental mathematical principles of quantum control to help develop a robust intuition about controlled quantum systems. The phenomena that will be studied include the role of dispersion in the control process and semiclassical approximations of the quantum dynamics. Motivated by the observation that a fair share of our intuition about quantum systems is derived from a few simple textbook systems that can be treated explicitly, the focus will be on simple one-dimensional systems, such as the infinite square well and the harmonic oscillator.