Anomalous thermal conduction in one dimension: a quantum calculation

Santhosh, G. ; Deepak Kumar, (2007) Anomalous thermal conduction in one dimension: a quantum calculation Physical Review E, 6 (2). 21105_1-21105_9. ISSN 1063-651X

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In this paper, we study the thermal conductivity of an anharmonically coupled chain of atoms. Numerical studies using classical dynamics have shown that the conductivity of a chain with nearest neighbor couplings diverges with chain length L as Lα; earlier studies found α≈0.4 under a range of conditions, but a recent study on longer chains claims α=1/3. Analytically, this problem has been studied by calculating the relaxation rate Γq of the normal modes of vibration as a function of its wave vector q. Two theoretical studies of classical chains, one using the mode-coupling formulation and the other the Boltzmann equation method, led to Γq?q5/3, which is consistent with α=0.4. Here we study the problem for a quantum anharmonic chain with quartic anisotropy. We develop a low-temperature expansion for Γq and find that, in the regime ωq«kBT, Γq∝q5/3T2, where ωq is the frequency of the mode. In our analysis, the relaxation arises due to umklapp scattering processes. We further evaluate the thermal conductivity of the chain using the Kubo formula, which enables us to take into account the transport relaxation time through vertex corrections for the current-current correlator. This calculation also yields α=0.4.

Item Type:Article
Source:Copyright of this article belongs to American Physical Society.
ID Code:9861
Deposited On:02 Nov 2010 10:36
Last Modified:31 May 2011 09:20

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