Heat transport in harmonic lattices

Details Heat transport in harmonic lattices Heat transport in harmonic lattices

2006-06-19

arxiv.org/abs/cond-mat/0606465v3

J. Stat. Phys., vol. 125, 801 (2006)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

One misprint and one error have been corrected; 22 pages, 2 figures

Scientific paper

10.1007/s10955-006-9235-3

We work out the non-equilibrium steady state properties of a harmonic lattice which is connected to heat reservoirs at different temperatures. The heat reservoirs are themselves modeled as harmonic systems. Our approach is to write quantum Langevin equations for the system and solve these to obtain steady state properties such as currents and other second moments involving the position and momentum operators. The resulting expressions will be seen to be similar in form to results obtained for electronic transport using the non-equilibrium Green's function formalism. As an application of the formalism we discuss heat conduction in a harmonic chain connected to self-consistent reservoirs. We obtain a temperature dependent thermal conductivity which, in the high-temperature classical limit, reproduces the exact result on this model obtained recently by Bonetto, Lebowitz and Lukkarinen.

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