Heat Transport in Ordered Harmonic Lattices |
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Authors: | Dibyendu Roy Abhishek Dhar |
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Institution: | (1) Raman Research Institute, Bangalore, 560080, India |
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Abstract: | We consider heat conduction across an ordered oscillator chain with harmonic interparticle interactions and also onsite harmonic
potentials. The onsite spring constant is the same for all sites excepting the boundary sites. The chain is connected to Ohmic
heat reservoirs at different temperatures. We use an approach following from a direct solution of the Langevin equations of
motion. This works both in the classical and quantum regimes. In the classical case we obtain an exact formula for the heat
current in the limit of system size N→∞. In special cases this reduces to earlier results obtained by Rieder, Lebowitz and Lieb and by Nakazawa. We also obtain
results for the quantum mechanical case where we study the temperature dependence of the heat current. We briefly discuss
results in higher dimensions. |
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Keywords: | Harmonic crystal Langevin equations Ohmic baths Heat conduction |
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