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Chapitre D'ouvrage Année : 2016

Thermal conductivity in harmonic lattices with random collisions

Résumé

We review recent rigorous mathematical results about the macroscopic behaviour of harmonic chains with the dynamics perturbed by a random exchange of velocities between nearest neighbor particles. The random exchange models the effects of nonlinearities of anharmonic chains and the resulting dynamics have similar macroscopic behaviour. In particular there is a superdiffusion of energy for unpinned acoustic chains. The corresponding evolution of the temperature profile is governed by a fractional heat equation. In non-acoustic chains we have normal diffusivity, even if momentum is conserved.
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Dates et versions

hal-01196009 , version 1 (08-09-2015)
hal-01196009 , version 2 (23-12-2015)

Identifiants

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Giada Basile, Cédric Bernardin, Milton Jara, Tomasz Komorowski, Stefano Olla. Thermal conductivity in harmonic lattices with random collisions. Stefano Lepri. Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer, 921, Springer, pp.215, 2016, Springer Lecture Notes in Physics, 978-3-319-29259-5. ⟨10.1007/978-3-319-29261-8_5⟩. ⟨hal-01196009v2⟩
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