Theory of Fractional Statistics

9413057对分数统计物理进行理论和计算研究。这项工作建立在先前对任意子超导性的研究基础上，并对分数量子霍尔效应的物理学做出了贡献。提出了三个具体项目：(1)用量子蒙特卡罗方法研究任意子的金属-绝缘体跃迁；(2)一个新的量子数的物理学，它是希尔伯特空间不相容的度量，即泡利原理的推广；(3)耗散映射在金属和绝缘体中多型叠加问题中的应用。本理论研究将集中于具有分数统计量的粒子的研究，即与现实世界中常见粒子不同的粒子。然而，有证据表明，这些粒子存在于特殊情况下，也可能是其他更常见现象的基础。这项研究将研究这些粒子的基础，并研究它们的一些可能的表现。额外的努力也将花费在研究各种复杂的材料系统使用一种新的技术，从非线性动力学。

9413057 Theoretical and computational research will be conducted on the physics of fractional statistics. The work builds on previous research on anyon superconductivity and contributes to the physics of the fractional quantum Hall effect. Three specific projects are proposed: (1) A quantum Monte Carlo study of the metal-insulator transition for anyons; (2) The physics of a new quantum number which is a measure of Hilbert space exclusion, that is, a generalization of the Pauli Principle; (3) The application of a dissipative mapping to the problem of stacking polytypes in metals and insulators. %%% This theoretical research will focus on the study of particles with fractional statistics, that is, particles unlike the common ones found in the real world. However, there is evidence that these particles exist under special circumstances and may also underlay other more common phenomena. This research will study the foundations of these particles and study a number of their possible manifestations. Additional effort will also be expended in investigating various complex materials systems using a new technique derived from nonlinear dynamics.