Theoretical Research in Statistical Mechanics

将对具有拓扑量子数的系统的各个方面进行理论研究。对量子霍尔效应的研究将继续进行，霍尔器件中的电流是在哪里产生的问题应该得到澄清。二维调制系统中的量子霍尔效应与相变理论之间的类比工作也将继续进行。关于超流氦中量子化涡旋在极低温度下的运动的新工作正在开始。本课程将对拓扑量子数进行全面的回顾。将对各种量子效应的含义和原因进行理论研究。要研究的系统包括二维电子气及其通过量子霍尔效应和超流氦的表现。各种缺陷结构，如涡旋的影响，将是这项工作的重点。

Theoretical research will be conducted on various aspects of systems which have topological quantum numbers. Research on the quantum Hall effect will be continued and the question of where the current is generated in a Hall device should be clarified. Work on the analogy between the quantum Hall effect in a two-dimensionally modulated system and the theory of phase transitions will also be continued. New work on the motion of quantized vortices in superfluid helium at very low temperatures is being started. A comprehensive review of topological quantum numbers will be written. %%% Theoretical research will be conducted on the meaning and cause of various quantum effects. Systems to be investigated include the two-dimensional electron gas and its manifestation through the quantum Hall effect and superfluid helium. The influence of various defect structures, such as vortices, will be the focus of this work.