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We derive the thermal conductivities of one-dimensional harmonic andanharmonic lattices with self-consistent heat baths (BRV lattice) from theSingle-Mode Relaxation Time (SMRT) approximation. For harmonic lattice, weobtain the same result as previous works. However, our approach is heuristicand reveals phonon picture explicitly within the heat transport process. Theresults for harmonic and anharmonic lattices are compared with numericalcalculations from Green-Kubo formula. The consistency between derivation andsimulation strongly supports that effective (renormalized) phonons are energycarriers in anharmonic lattices although there exist some other excitationssuch as solitons and breathers.

Thermal conductivity of one-dimensional lattices with self-consistent heat baths: a heuristic derivation