论文标题
一维riesz气体的配对相关函数
Pair correlation function of the one-dimensional Riesz gas
论文作者
论文摘要
从随机矩阵理论中的一种方法用于计算$ n \ gg 1 $的一维气体的配对相关函数，具有功率定律的拒绝相互作用潜在的$ u（x）\ propto | x |^{ - s} $（socalled riesz ass as sopalled riesz ass as）。获得了单粒子操作员协方差的整体公式，该公式将在限制$ s \ rightarrow -1 $（库仑气）和$ s \ rightarrow 0 $（log-gas）中概括为已知结果。作为应用程序，我们计算了Riesz气体质量中心的方差，该质量具有通用的较大$ n $限制，不取决于限制电位的形状。
A method from random-matrix theory is used to calculate the pair correlation function of a one-dimensional gas of $N\gg 1$ classical particles with a power law repulsive interaction potential $u(x)\propto |x|^{-s}$ (a socalled Riesz gas). An integral formula for the covariance of single-particle operators is obtained which generalizes known results in the limits $s\rightarrow -1$ (Coulomb gas) and $s\rightarrow 0$ (log-gas). As an application, we calculate the variance of the center of mass of the Riesz gas, which has a universal large-$N$ limit that does not depend on the shape of the confining potential.
