Heat Transport in Harmonic Lattices
 Abhishek Dhar,
 Dibyendu Roy
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We work out the nonequilibrium 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 nonequilibrium Green’s function formalism. As an application of the formalism we discuss heat conduction in a harmonic chain connected to selfconsistent reservoirs. We obtain a temperature dependent thermal conductivity which, in the hightemperature classical limit, reproduces the exact result on this model obtained recently by Bonetto, Lebowitz and Lukkarinen.
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 Title
 Heat Transport in Harmonic Lattices
 Journal

Journal of Statistical Physics
Volume 125, Issue 4 , pp 801820
 Cover Date
 20061101
 DOI
 10.1007/s1095500692353
 Print ISSN
 00224715
 Online ISSN
 15729613
 Publisher
 Kluwer Academic PublishersPlenum Publishers
 Additional Links
 Topics
 Keywords

 Harmonic crystal
 quantum Langevin equations
 nonequilibrium Green’s function
 Fourier’s law
 Industry Sectors
 Authors

 Abhishek Dhar ^{(1)}
 Dibyendu Roy ^{(1)}
 Author Affiliations

 1. Raman Research Institute, Bangalore, 560080, India