  We study the heat transport properties of a chain of coupled quantum harmonic
oscillators in contact at its ends with two heat reservoirs at distinct
temperatures. Our approach is based on the use of an evolution equation for the
density operator which is a canonical quantization of the classical
Fokker-Planck-Kramers equation. We set up the evolution equation for the
covariances and obtain the stationary covariances at the stationary states from
which we determine the thermal conductance in closed form when the
interparticle interaction is small. The conductance is finite in the
thermodynamic limit implying an infinite thermal conductivity.
