Simulation of Nonharmonic Interactions in a Crystal by Self-Consistent Reservoirs

Independent heat reservoirs are postulated to interact with the atoms in a harmonic system as a substitute for real nonharmonic forces. The temperature of each reservoir is determined by the condition that it exchange no energy with the system in the steady state. An explicit solution for the covariance matrix is obtained for the case of the linear chain. The thermal conductivity is finite and inversely proportional to the coupling to the reservoirs.