The effect of impurity scattering on the dielectric constant of the 1-D quantum sine-Gordon system is investigated with the use of the fermion representation of the boson fields. We find that the impurity scattering gives rise to the increase of the dielectric constant.
The dynamical behavior of the one-dimensional quantum sine-Gordon system with a misfit parameter is investigated at a particular value of the quantum parameter g2=4π. For this purpose the dynamical correlation functions are calculated by using the Fermi-Bose relation. From the behavior of the displacement correlation function we find that the thermal velocity is given by ∼√T/m0 in the commensurate state (m0-| µ 8730|≫T) or in the cross-over region (m0≃| µ \tilde |≫T) and approaches value 1 as T or | µ \tilde | is increased. Here m0 and µ \tilde, respectively, are the gap and the chemical potential in the corresponding fermion system. For the case of denity-density correlation function, we give in the commensurate state expressions which are similar to those derived on the basis of the soliton phenomenology in the classical system. A particular case of the density-density correlation function is discussed in detail by following another route.