论文标题
分数统计
Fractional Statistics
论文作者
论文摘要
粒子组件的量子力学描述，其运动仅限于两个（或一个）空间维度的粒子组件提供了许多与玻色子和费米子不同的可能性。我们称这种颗粒为AYON。最简单的Anyons通过角相参数$θ$进行了参数化。 $θ= 0，π$分别对应于玻色子和费米子；在中间值，我们说我们具有分数统计数据。在两个维度中，$θ$将波函数获取的相位描述为两个逆时针彼此缠绕的。它为相对角动量产生允许值的变化。与Abelian U（1）量规组相关的局部电荷和磁通量的复合材料实现了这种行为。更复杂的充电升华结构可能涉及在允许的电荷和通量范围内作用的非亚伯和产品组，从而产生非亚伯和相互统计。非亚伯亚人的互换在内部状态的新兴空间内实施了波函数的单一转换。包括Chern-simons术语的量子场理论描述了各种的任何人。环上的一维任何人的交叉点是单向的，因此在互换时获得的分数相$θ$会导致Anyons之间相对动量的分数移动。长期以来，已经预测将包括任何人。最近，在散射和干涉实验中，已经观察到$ν= 1/3 $分数量子霍尔在$ν= 1/3 $中预测的任何行为。设计系统中的激发，特别是包括超导电路，可以表现出任何行为。此类系统正在开发供量子信息处理中使用。
The quantum-mechanical description of assemblies of particles whose motion is confined to two (or one) spatial dimensions offers many possibilities that are distinct from bosons and fermions. We call such particles anyons. The simplest anyons are parameterized by an angular phase parameter $θ$. $θ= 0, π$ correspond to bosons and fermions respectively; at intermediate values we say that we have fractional statistics. In two dimensions, $θ$ describes the phase acquired by the wave function as two anyons wind around one another counterclockwise. It generates a shift in the allowed values for the relative angular momentum. Composites of localized electric charge and magnetic flux associated with an abelian U(1) gauge group realize this behavior. More complex charge-flux constructions can involve non-abelian and product groups acting on a spectrum of allowed charges and fluxes, giving rise to nonabelian and mutual statistics. Interchanges of non-abelian anyons implement unitary transformations of the wave function within an emergent space of internal states. Anyons of all kinds are described by quantum field theories that include Chern--Simons terms. The crossings of one-dimensional anyons on a ring are uni-directional, such that a fractional phase $θ$ acquired upon interchange gives rise to fractional shifts in the relative momenta between the anyons. The quasiparticle excitations of fractional quantum Hall states have long been predicted to include anyons. Recently the anyon behavior predicted for quasiparticles in the $ν= 1/3$ fractional quantum Hall state has been observed both in scattering and in interferometric experiments. Excitations within designed systems, notably including superconducting circuits, can exhibit anyon behavior. Such systems are being developed for possible use in quantum information processing.
