Limited validity of the Kubo formula for thermal conduction in modular quantum systems

The Kubo formula describes a current as a response to an external field. In the case of heat conduction there is no such external field. We analyze why and to what extent it is nevertheless justified to describe heat conduction in modular quantum systems by the Kubo formula. We call systems "modular" that may be described as consisting of weakly coupled identical subsystems. We explain in what sense this description applies to a large class of systems. Furthermore, we numerically evaluate the Kubo formula for some finite modular systems. We compare the results with data obtained from the direct numerical solution of the corresponding time-dependent Schrodinger equation.