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

Abstract

We derive the thermal conductivities of one-dimensional harmonic and anharmonic lattices with self-consistent heat baths (BRV lattice) from the Single-Mode Relaxation Time (SMRT) approximation. For harmonic lattice, we obtain the same result as previous works. However, our approach is heuristic and reveals phonon picture explicitly within the heat transport process. The results for harmonic and anharmonic lattices are compared with numerical calculations from Green-Kubo formula. The consistency between derivation and simulation strongly supports that effective (renormalized) phonons are energy carriers in anharmonic lattices although there exist some other excitations such as solitons and breathers.

4 pages, 3 figures. accepted for publication in JPSJ

References in corpus (7)

• Thermal conduction in classical low-dimensional lattices
• Heat transport in harmonic lattices
• Fourier's Law for a Harmonic Crystal with Self-consistent Stochastic Reservoirs
• q-Breathers and the Fermi-Pasta-Ulam Problem
• FPU $\beta$ model: Boundary Jumps, Fourier's Law and Scaling
• Heat conduction in 1D lattices with on-site potential
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Cited by in corpus (5)

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• Thermal conductivities of one-dimensional anharmonic/nonlinear lattices: renormalized phonons and effective phonon theory
• Temperature dependence of thermal conductivities of coupled rotator lattice and the momentum diffusion in standard map
• Temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with soft on-site potential