Solving 1d plasmas and 2d boundary problems using Jack polynomials and functional relations

TL;DR

This paper develops analytical methods to solve 1D plasmas and 2D boundary problems using Jack polynomials and functional relations, providing explicit calculations of free energy, conductance, and correlation functions.

Contribution

It introduces a novel combination of perturbative Jack polynomial techniques and non-perturbative Bethe ansatz methods for boundary Coulomb gases.

Findings

Explicit virial expansion coefficients for free energy and conductance

Discovery of a fluctuation-dissipation relation between free energy and conductance

Calculation of correlation functions in the boundary plasma model

Abstract

The general one-dimensional ``log-sine'' gas is defined by restricting the positive and negative charges of a two-dimensional Coulomb gas to live on a circle. Depending on charge constraints, this problem is equivalent to different boundary field theories. We study the electrically neutral case, which is equivalent to a two-dimensional free boson with an impurity cosine potential. We use two different methods: a perturbative one based on Jack symmetric functions, and a non-perturbative one based on the thermodynamic Bethe ansatz and functional relations. The first method allows us to compute explicitly all coefficients in the virial expansion of the free energy and the experimentally-measurable conductance. Some results for correlation functions are also presented. The second method provides in particular a surprising fluctuation-dissipation relation between the free energy and the conductance.