Correlation functions of the 1-D coulomb gas, solitons and the 1-D Fermi gas

Abstract

We study various correlation functions of the classical one-dimensional two component Coulomb gas (1-D CG). As a first example the dielectric function eq is considered. Explicit expressions for the first two terms of the long-wavelength expansion ofeq-1 are rigorously derived by extending the method of Edwards and Lenard. On account of the equivalence between the 1-D CG and the sine-Gordon (SG) model eq can also be viewed as a correlation function of the SG fieldφ and the effects of small amplitude oscillations and of solitons can be traced in eq. We show that the nonmetallic nature of the 1-D CG is solely attributable to solitons. A similar analysis is carried out for other correlation functions. We establish a relation between these correlation functions and certain response functions of a one-dimensional Fermi gas by exploiting the known equivalence between the backward-scattering model of the Fermi gas and a 2-D CG on the surface of a cylinder and by investigating the conditions under which this 2-D CG can be considered one-dimensional.