2010/04/16 by S. Gopalakrishnan, Santhosh G, Deepak Kumar +2
Materials Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Advanced Thermoelectric Materials and Devices #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Thermal properties of materials #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.1004.2749
arxiv created 2010/04/16 · openalex publication_date 2010/04/16 · arxiv updated 2010/04/19 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
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) ∝ N1/2.