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Through an exact analysis using quantum Langevin dynamics, we demonstrate thecrossover from ballistic to diffusive thermal transport in a harmonic chainwith each site connected to Ohmic heat reservoirs. The temperatures of the twoheat baths at the boundaries are specified from before whereas the temperaturesof the interior heat reservoirs are determined self-consistently by demandingthat in the steady state, on average, there is no heat current between any such(self-consistent) reservoir and the harmonic chain. Essence of our study isthat the effective mean free path separating the ballistic regime of transportfrom the diffusive one emerges naturally.

physical review. e, statistical, nonlinear and soft matter physics

Crossover from ballistic to diffusive thermal transport in quantum  Langevin dynamics study of a harmonic chain connected to self-consistent  reservoirs