Conductivity of a nonlinear Luttinger liquid with a large-scaled random potential

We perform a calculation of the uniform conductivity of one-dimensional degenerate fermion system with some large-scaled disorder. We use the nonlinear Luttinger liquid model. The only important limitation is that the frequency has to be large enough. Apart from that and few other minor constraints, the calculation is fairly general. For instance, we neither assume the interaction to be point-like nor weak. As a result, we obtain conductivity across a wide range of parameters, the parameters are the disorder scale, frequency, interaction radius and temperature.