  We present an exact solution for the heat conductance along a harmonic chain
connecting two reservoirs at different temperatures. In this model, the end
points correspond to Brownian particles with different damping coefficients.
Such analytical expression for the heat conductance covers its behavior from
mesoscopic to very long one-dimensional quantum chains, and validates the
ballistic nature of the heat transport in the latter example. This implies the
absence of the Fourier law for classical and quantum harmonic chains. We also
provide a thorough analysis of the normal modes of system which helps us to
satisfactorily interpret these results.
