Heat transport in harmonic lattices

Dhar, Abhishek ; Roy, Dibyendu (2006) Heat transport in harmonic lattices Journal of Statistical Physics, 125 (4). pp. 801-820. ISSN 0022-4715

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Official URL: http://www.springerlink.com/content/pv76ghp0725p72...

Related URL: http://dx.doi.org/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.

Item Type:Article
Source:Copyright of this article belongs to Springer.
Keywords:Harmonic Crystal; Quantum Langevin Equations; Non-equilibrium Green's Function; Fourier's Law
ID Code:79677
Deposited On:28 Jan 2012 12:09
Last Modified:18 May 2016 21:57

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