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

TL;DR

This paper presents a heuristic derivation of thermal conductivities in one-dimensional lattices with self-consistent heat baths, emphasizing the phonon picture and validating results with numerical simulations.

Contribution

It introduces a heuristic derivation method for thermal conductivity in 1D lattices that explicitly reveals phonon contributions and aligns with numerical results.

Findings

Heuristic derivation matches previous results for harmonic lattices.

Effective phonons are confirmed as primary energy carriers in anharmonic lattices.

Numerical simulations support the phonon-based heat transport mechanism.

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.