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及其更复杂的相关量子场论中的几个问题。我的工作可以被认为是在两个领域：量子场论和应用，以及量子信息(前者的权重比后者更大)。我正在做三个项目，大致属于量子场论的范畴。第一种是一种被称为约瑟夫森效应的现象的场论描述，这种现象会在被绝缘体隔开的两个超导体之间产生电流。这种描述很有趣，因为它可以很容易地推广到更复杂的环境(具有所谓的非阿贝尔序参数)，正如我和同事们所演示的那样。我打算加深我们对这一描述的理解，并找到非阿贝尔效应在真实物理系统中的应用。第二个是研究被称为阿贝尔希格斯模型的玩具场理论中的可能阶段，增加了一个所谓的Chern-Simons项。(玩具模型之所以被研究，不是因为它描述了一个真实的物理系统，而是因为它比现实模型更简单，因此更容易进行数学分析，希望这样的分析将有助于揭示更现实的模型。在我们的例子中，玩具模型只存在于两个空间维度中。)研究模型的相结构是很有趣的，因为不同的相具有非常不同的性质；一个例子是夸克(质子、中子和其他不太熟悉的粒子的成分)相互作用模型中的禁闭转变。第三个项目是继续研究拓扑缺陷对虚真空衰变的影响。虚真空是一种经典意义上的稳定，但通过量子力学隧穿而不稳定的真空。虽然这看起来与现实相去甚远，但它实际上很像任何相变中发生的事情，特别是在已知发生在早期宇宙中的相变中。我最近一直在研究这个问题，还有很多工作要做。有两个项目研究量子力学问题，着眼于量子信息。其中一个是，我正在研究量子力学中一种被称为绝热近似的近似的有效性，该近似适用于依赖时间但缓慢演化的系统。控制系统对依赖时间的外部效应的反应是这个游戏的名字。这种控制在量子力学中几乎是全面必要的，但在量子信息领域尤其如此，在量子信息领域，操纵量子比特(信息的量子力学单位)可以说是最重要的任务。第二个项目是研究自旋晶格，作为研究量子力学基础的工具，特别是贝尔定理。虽然第一个领域是我从事多年的工作，但第二个领域是我最近才开始考虑的。粗略的想法是考虑一个有限的自旋晶格，通常的主人公爱丽丝和鲍勃可以接触到自旋链或梯子末端的自旋。在这个模型中，中间自旋扮演了隐藏变量的角色，目的是研究Alice和Bob在这种情况下所做的测量之间的关联。

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. My work can be thought of as being in two fields: quantum field theory and applications, and quantum information (the former weighted more heavily than the latter). I am working on three projects falling roughly in the category of quantum field theory. The first is a field theoretic description of a phenomenon known as the Josephson effect, which gives rise to current flow between two superconductors separated by an insulator. This description is interesting because it can easily be generalized to a more complicated setting (one with what is known as a non-Abelian order parameter), as colleagues and I have demonstrated. I intend to deepen our understanding of this description, and to find applications of the non-Abelian effect to real physical systems. The second is a study of the possible phases in a toy field theory known as the Abelian Higgs model, with the addition of a so-called Chern-Simons term. (A "toy" model is one that is studied not because it describes a realistic physical system, but rather because it is simpler than realistic models, so it is easier to analyze mathematically, the hope being that such an analysis will shed light on more realistic models. In our case, the toy model is one that lives in only two space dimensions.) Studying the phase structure of a model is interesting because different phases have very different properties; one example is the confinement transition in the model of interactions among quarks (the constituents of protons, neutrons, and other less familiar particles). The third project is to continue studying the effect of topological defects on false vacuum decay. A false vacuum is one that is stable classically but unstable via tunnelling quantum mechanically. While this might seem far removed from reality, it is actually much like what happens in any phase transition, and particularly in the phase transitions that were known to occur in the early universe. I have worked on this problem in the recent past, and there is much still to be done. Two projects study quantum mechanical issues, with an eye towards quantum information. In one, I am studying the validity of an approximation in quantum mechanics known as the adiabatic approximation, which applies to time-dependent, yet slowly-evolving, systems. Controlling the reaction of the system to time-dependent external effects is the name of the game. This control is necessary almost across the board in quantum mechanics, but it is particularly at the forefront in quantum information, where manipulation of qubits (quantum-mechanical units of information) is arguably the most important task to master. The second project is to study spin lattices as a tool for investigation the foundations of quantum mechanics, and specifically Bell's Theorem. While the first of these is an area I have worked on for several years, the second is something I have begun to think about only recently. The rough idea is to consider a finite lattice of spins, the usual protagonists Alice and Bob having access to spins at the ends of a spin chain or ladder. In this model, the intermediate spins play the role of hidden variables, and the objective is to study correlations between measurements made by Alice and Bob in this setting.