Mathematical theory of complex open quantum systems

物理物体(分子、原子、电子、原子核、光子等)总是受到周围环境的影响。一般来说，一个系统越小，这种影响就越重要。量子系统特别小，因此环境对它们的影响是非常丰富和重要的。环境可以改变在理论和实验中非常重要的基本性质(在量子信息理论、量子计算、量子测量甚至医学成像中的应用)。 在我的研究中，我试图找到数学方程，精确地描述量子物体与环境接触时的行为。我对“复杂开放系统”特别感兴趣，因为它们出现在许多现实世界的应用程序中。例如，在核磁共振成像中，要检查的生物组织样本至少含有大约10的23(！)次方。原子或分子。要描述它们中的每一个是不可能的。因此，重要的是获得管控这类系统行为的有用的物理或化学(但实际上是数学)“定律”。 我的研究是纯数学的，但它对应用感兴趣，例如，在努力创造建造量子计算机所需的新材料方面。

Physical objects (molecules, atoms, electrons, nuclei, photons, etc) are constantly subject to the influence of their surroundings. Generally, the smaller a system, the more important this influence. Quantum systems are particularly small and so the influence of surroundings (environments) on them is very rich and important. Surroundings can change fundamental properties that are of great importance in theory and experiments (with applications in quantum information theory, quantum computing, quantum measurement and even medical imaging). In my research, I try to find mathematical equations describing, with precision, how quantum objects behave when in contact with an environment. I am particularly interested in "complex open systems" as they appear in many real world applications. For instance, in nuclear magnetic resonance imaging, a sample of biological tissue to be examined contains at least roughly 10 to the power 23 (!) atoms or molecules. To describe each and every one of them is impossible. So it is important to obtain useful physical or chemical (but really, mathematical) "laws" that govern the behaviour of such systems. My research is purely mathematical, but it is of interest in applications, for example, in the effort to create new materials necessary in the construction of quantum computers.