Approximative analytical method for some Langevin dynamical systems

We develop an approach which leads to an analytically treatable integral representation for the steady state correlation functions of some Langevin dynamical systems, which are related to the microscopic Hamiltonian description of the heat mechanism. For the simpler case of harmonic interactions (where rigorous results exist and a comparison with our method is possible), we perform the computations for the thermal conductivity (given by two-point functions) and show that our approximative scheme works perfectly well.