  We consider heat conduction across an ordered oscillator chain with harmonic
interparticle interactions and also onsite harmonic potentials. The onsite
spring constant is the same for all sites excepting the boundary sites. The
chain is connected to Ohmic heat reservoirs at different temperatures. We use
an approach following from a direct solution of the Langevin equations of
motion. This works both in the classical and quantum regimes. In the classical
case we obtain an exact formula for the heat current in the limit of system
size N to infinity. In special cases this reduces to earlier results obtained
by Rieder, Lebowitz and Lieb and by Nakazawa. We also obtain results for the
quantum mechanical case where we study the temperature dependence of the heat
current. We briefly discuss results in higher dimensions.
