  In d-dimensional lattices of coupled quantum harmonic oscillators, we analyze
the heat current caused by two thermal baths of different temperature, which
are coupled to opposite ends of the lattice, with focus on the validity of
Fourier's law of heat conduction. We provide analytical solutions of the heat
current through the quantum system in the non-equilibrium steady state using
the rotating-wave approximation and bath interactions described by a master
equation of Lindblad form. The influence of local dephasing in the transition
of ballistic to diffusive transport is investigated.
