Journal of Statistical Physics

, Volume 125, Issue 4, pp 801–820

Heat Transport in Harmonic Lattices


DOI: 10.1007/s10955-006-9235-3

Cite this article as:
Dhar, A. & Roy, D. J Stat Phys (2006) 125: 801. doi: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.


Harmonic crystal quantum Langevin equations non-equilibrium Green’s function Fourier’s law 

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Raman Research InstituteBangaloreIndia

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