论文标题
我们应该如何在模拟中选择边界条件，以在一个和二维中检测到任何人？
How should we choose the boundary conditions in a simulation which could detect anyons in one and two dimensions?
论文作者
论文摘要
从统计物理学的角度来看，我们讨论了一个和两个空间维度中任何一个空间维度的问题。特别是我们想了解蒙特卡洛模拟中必需的扭曲的周期性边界条件的选择如何模仿许多身体系统的热力学极限会影响颗粒的统计性质。当将配置空间简单地连接为例如线上的粒子时，颗粒可以只是玻色子。它们可以是玻色子和费米子，当配置空间被双重连接时，例如，对于三维空间中的颗粒，或者在属的riemannian属表面上，大或等于一个（在圆环上等等。）。当配置空间与平面上或圆圈中的粒子无限连接时，它们可以是具有任意统计数据的标量。当配置空间是球体上的一个粒子时，它们可以是具有分数统计的标量。当配置空间双重连接时，与大于或等于一个属的riemannian表面上的颗粒相连时，可以进一步具有具有分数统计的多组分。我们确定了各种几何形状上硬核颗粒（包括anyons）的规范分区函数的表达。然后，我们展示一个在一个和二维中的边界条件（周期性或开放）的选择如何确定在考虑的表面上可以存在哪些粒子。总而言之，我们提到了Laughlin波函数，并给出了一些有关实验的评论。
We discuss the problem of anyonic statistics in one and two spatial dimensions from the point of view of statistical physics. In particular we want to understand how the choice of the Bornvon Karman or the twisted periodic boundary conditions necessary in a Monte Carlo simulation to mimic the thermodynamic limit of the many body system influences the statistical nature of the particles. The particles can either be just bosons, when the configuration space is simply connected as for example for particles on a line. They can be bosons and fermions, when the configuration space is doubly connected as for example for particles in the tridimensional space or in a Riemannian surface of genus greater or equal to one (on the torus, etc . . . ). They can be scalar anyons with arbitrary statistics, when the configuration space is infinitely connected as for particles on the plane or in the circle. They can be scalar anyons with fractional statistics, when the configuration space is the one of particles on a sphere. One can further have multi components anyons with fractional statistics when the configuration space is doubly connected as for particles on a Riemannian surface of genus greater or equal to one. We determine an expression for the canonical partition function of hard core particles (including anyons) on various geometries. We then show how the choice of boundary condition (periodic or open) in one and two dimensions determine which particles can exist on the considered surface. In the conclusion, we mention the Laughlin wavefunction and give a few comments about experiments.
