Quantum theory and applications

量子力学基本上支配着微观尺度及以下的所有现象。我打算研究量子力学中的几个问题，以及它更为复杂的相关理论——量子场论。其中两个问题是在孤子的背景下，孤子是经典场论的扩展解，其行为类似于粒子。虽然本质上不是量子力学，但这些对象也存在于量子场论中。另一个研究项目是从场论的角度来看超导中的约瑟夫森效应，以及将这种效应推广到潜在对称性为非阿贝尔类型的情况。将原子核聚集在一起的强相互作用的一个重要特性是约束，即某些基本粒子（夸克和胶子）不能彼此分离。这个性质被广泛接受，因为它很难被实际证明。我正在进行的两个项目是研究玩具模型，它们可能有也可能没有这种特性；从玩具模型中学到的东西，希望能对更现实的模型有所启发。另一项研究工作对我来说代表了一点方向的改变，朝着量子信息，一个新的、充满活力的研究领域。我正在研究的一个具体问题是量子力学中所谓绝热定理的有效性条件。这个定理早在量子力学的早期就已经为人所知，然而，它有效的确切条件最近才受到仔细研究。其次，我正在研究利用经典通信在纠缠量子系统上模拟广义量子测量，这是量子信息和量子通信领域非常感兴趣的课题。

Quantum mechanics governs essentially all phenomena at microscopic scales and below. I intend to examine several problems in quantum mechanics and its more sophisticated relative, quantum field theory.Two of these problems are in the context of solitons, which are extended solutions of classical field theory which resemble particles in their behaviour. While not intrinsically quantum mechanical, these objects exist in quantum field theory as well.Another research project pertains to the Josephson effect in superconductivity from a field theory perspective, as well as a generalization of this effect to situations where the underlying symmetry is of a type known as non-abelian.An important property of the strong interaction which holds nuclei together is confinement, the fact that certain fundamental particles (quarks and gluons) cannot be isolated from one another. This property is as widely accepted as it is difficult to actually prove. Two projects on which I am working study toy models which may or may not have this property; what is learned from the toy models will hopefully shed light on more realistic models.Anoher research effort represents a bit of a change of direction for me, towards quantum information, a new and vigourous field of research. One specific problem I am investigating is the conditions of validity of the so-called adiabatic theorem in quantum mechanics. This theorem has been known since the early days of quantum mechanics, yet the exact conditions under which it is valid have come under scrutiny lately. Secondly, I am studying the simulation of generalized quantum measurements on an entangled quantum system using classical communication, which is a subject of great interest in quantum information and quantum communication.