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date: 19 August 2019

Abstract and Keywords

This article focuses on the phonon transport or thermal transport of small systems, including quasi-one-dimensional systems such as carbon nanotubes. The Fourier law well describes the thermal transport phenomena in normal bulk materials. However, it is no longer valid when the sample dimension reduces down to below the mean-free path of phonons. In such a small system, the phonons propagate coherently without interference with other phonons. The article first considers the Boltzmann–Peierls formula of diffusive phonon transport before discussing coherent phonon transport, with emphasis on the Landauer formulation of phonon transport, ballistic phonon transport and quantized thermal conductance, numerical calculation of the phonon-transmission function, and length dependence of the thermal conductance.

Keywords: phonon transport, thermal transport, small systems, carbon nanotubes, phonons, Boltzmann–Peierls formula, Landauer formula, thermal conductance, phonon-transmission function, length dependence

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