ELECTRICAL AND THERMAL-CONDUCTIVITIES OF THE DISORDERED ONE-DIMENSIONAL QUANTUM SINE-GORDON SYSTEM (G(2)=4-PI)

We consider the zero frequency electrical and the thermal conductivity of the disordered one-dimensional quantum sine-Gordon system (g(2) = 4 pi) with use of a Fermi-Bose relation and a self-consistent t matrix approximation. Two types of impurities are discussed. We find that the behavior of the ''Lorenz'' number is very different from the other when the gap energy omega(g) is finite. At low temperatures one type of impurities gives the ''Lorenz'' number alpha similar to (omega g/T)(2), while the other one gives alpha similar to 2.