  We consider a class of one-dimensional chains of weakly coupled many level
systems. We present a theory which predicts energy diffusion within these
chains for almost all initial states, if some concrete conditions on their
Hamiltonians are met. By numerically solving the time dependent Schroedinger
equation, we verify this prediction. Close to equilibrium we analyze this
behavior in terms of heat conduction and compute the respective coefficient
directly from the theory.

Statistical Mechanics;Quantum Physics