Topological Quantum Numbers

9528345尽管如此，这是一项继续研究材料理论中两个基本问题的建议，即量子霍尔效应和超导电性。这里的具体问题都是由拓扑对称性导出的守恒定律和相应的量子数推导出来的。需要解决的问题包括，电流在霍尔器件和超流或超导体中产生的位置，涡旋的质量密度问题，以及涡旋上的马格努斯力是有限的还是零的。此外，还将探索量子混沌的某些方面，例如量子力学中两个态之间的距离的概念。许多计量工作(从基本常数的测量到高精度的测量，或高精度的电压和电阻测量)涉及到拓扑量子数的使用。这些量子数在各种不同的情况下都能找到，但在本质上有很深的相似之处。与拓扑量子数相关的基本性质是本研究的主题。这些应用包括超导体或超流体的稳定性，更具体地说，是涡旋的详细动力学。本课程将以课堂讲稿和有关拓扑量子数主题的经典论文重印的形式，准备一篇全面的复习。

9528345 Thouless This is a proposal to continue work on two fundamental problems in materials theory, quantum Hall effect and superconductivity. The specific problems here are all derived from the topological symmetry derived conservation laws and the corresponding quantum numbers. The questions that need to be addressed, include the location where the current is generated in a Hall device and in a superfluid or a superconductor, the question of the mass density of a vortex and whether the Magnus force on a vortex is finite or zero. In addition there will be exploration of some aspects of quantum chaos, for example the notion of a distance between two states in quantum mechanics. %%% Much of the metrological work (measumenent of fundamental constants to high precision, or high precision measurements of voltage and resistance) involve use of topological quantum numbers. These quantum numbers are found in a variety of diverse situations and yet there are deep underlying similarities. The fundamental properties associated with the topological quantum numbers are the subject of this study. The applications include the stability of superconductor or a superfluid and more specifically the detailed dynamics of the vortices. A comprehensive review, in the form of lecture notes and reprints of classical papers on the subject of topological quantum numbers will be prepared.