Correlation functions of the 1-D coulomb gas,solitons and the 1-D Fermi gas |
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Authors: | W Apel H U Everts H Schulz |
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Institution: | (1) Institut für Theoretische Physik, Universität Hannover, Appelstraße 2, D-3000 Hannover, Federal Republic of Germany |
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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
q
is considered. Explicit expressions for the first two terms of the long-wavelength expansion of
q
-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
q
can also be viewed as a correlation function of the SG field and the effects of small amplitude oscillations and of solitons can be traced in
q
. 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. |
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