Santhosh, G. ; Deepak Kumar, (2010) Anomalous transport and phonon renormalization in a chain with transverse and longitudinal vibrations Physical Review E, 82 (1). 11130_1-11130_9. ISSN 1063-651X
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Official URL: http://pre.aps.org/abstract/PRE/v82/i1/e011130
Related URL: http://dx.doi.org/10.1103/PhysRevE.82.011130
Abstract
We study thermal transport in a chain of coupled atoms, which can vibrate in longitudinal as well as transverse directions. The particles interact through anharmonic potentials upto cubic order. The problem is treated quantum mechanically. We first calculate the phonon frequencies self-consistently taking into account the anharmonic interactions. We show that for all the modes, frequencies must have linear dispersion with wave vector q for small q irrespective of their bare dispersions. We then calculate the phonon relaxation rates Γi(q), where i is the polarization index of the mode, in a self-consistent approximation based on second-order perturbation diagrams. We find that the relaxation rate for the longitudinal phonon, Γx(q)∝q3/2, while that for the transverse phonon Γy(q)∝q2. The consequence of these results on the thermal conductivity κ(N) of a chain of N particles is that κ(N)∝N½.
Item Type: | Article |
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Source: | Copyright of this article belongs to American Physical Society. |
ID Code: | 9854 |
Deposited On: | 02 Nov 2010 10:37 |
Last Modified: | 16 May 2016 19:35 |
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