标题： 一维任意子的统计相位和动量间距 显示英文标题

标题： Statistical Phases and Momentum Spacings for One-Dimensional Anyons

摘要： 任意子和分数统计在二维系统中现在已经得到了充分的确认。 在一维系统中，到目前为止，分数统计仅通过哈德纳的分数排除原理得到证实，而不是通过粒子交换时波函数获得的分数相位。 从表面上看，配置空间的拓扑似乎排除了一维情况下的这种相位。 在这里，我们认为一维任意子的交叉总是单向的，这使得可以一致地分配相位，从而引入一个统计参数θ。 当施加周期性边界条件时，这种分数统计体现在任意子单粒子动量的分数间距上。 这些间距由Δp = 2πħ/L (|θ|/π + 非负整数) 给出，其中系统长度为L。这个条件是二维任意子相对角动量量子化l_z=ħ(-θ/π + 2整数)的类比。 显示英文摘要

摘要： Anyons and fractional statistics are by now well established in two-dimensional systems. In one dimension, fractional statistics has been established so far only through Haldane's fractional exclusion principle, but not via a fractional phase the wave function acquires as particles are interchanged. At first sight, the topology of the configuration space appears to preclude such phases in one dimension. Here we argue that the crossings of one-dimensional anyons are always unidirectional, which makes it possible to assign phases consistently and hence to introduce a statistical parameter theta. The fractional statistics then manifests itself in fractional spacings of the single-particle momenta of the anyons when periodic boundary conditions are imposed. These spacings are given by Delta p = 2 pi hbar/L (|theta|/pi+non-negative integer) for a system of length L. This condition is the analogue of the quantisation of relative angular momenta according to l_z=hbar(-theta/pi+2integer) for two-dimensional anyons.