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.

arXiv comment6 pages, 1 figure

References in corpus (7)

• Random-Matrix Theory of Quantum Transport
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Average Time Spent by Levy Flights and Walks on an Interval with Absorbing Boundaries
• Universality of Brezin and Zee's Spectral Correlator
• Harmonically confined particles with long-range repulsive interactions
• Universal covariance formula for linear statistics on random matrices
• Harmonically confined long-ranged interacting gas in the presence of a hard wall

Cited by in corpus (5)

• Noether-Constrained Correlations in Equilibrium Liquids
• Dynamical fluctuations in the Riesz gas
• Out of equilibrium dynamics of repulsive ranked diffusions: the expanding crystal
• Spatio-temporal fluctuations in the passive and active Riesz gas on the circle
• Full counting statistics of 1d short-range Riesz gases in confinement