  We consider chains consisting of several identical subsystems weakly coupled
by various types of next neighbor interactions. At both ends the chain is
coupled to a respective heat bath with different temperature modeled by a
Lindblad formalism. The temperature gradient introduced by this environment is
then treated as an external perturbation. We propose a method to evaluate the
heat current and the local temperature profile of the resulting stationary
state as well as the heat conductivity in such systems. This method is similar
to Kubo techniques used e.g. for electrical transport but extended here to the
Liouville space.
