Pair correlation function of the one-dimensional Riesz gas

Abstract

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 $s\to -1$ (Coulomb gas) and $s\to 0$ (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.

6 pages, 1 figure

References in corpus (1)

• Harmonically confined long-ranged interacting gas in the presence of a hard wall

Cited by in corpus (1)

• Out of equilibrium dynamics of repulsive ranked diffusions: the expanding crystal