2008/08/31 by Abhishek Dhar · 1 citation
Engineering · Materials Science · Physics and Astronomy · #Advanced Thermoelectric Materials and Devices #Thermal properties of materials #Thermoelastic and Magnetoelastic Phenomena #cond-mat.mes-hall #cond-mat.stat-mech
paper · pdf · doi:10.1080/00018730802538522
published as Advances in Physics, Vol. 57, No. 5, 457-537 (2008) · 78 pages, 25 figures, Review Article (revised version)
openalex publication_date 2008/09/01 · arxiv created 2008/11/19 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/02
Recent results on theoretical studies of heat conduction in low-dimensional systems are presented. These studies are on simple, yet non-trivial, models. Most of these are classical systems, but some quantum-mechanical work is also reported. Much of the work has been on lattice models corresponding to phononic systems, and some on hard-particle and hard-disc systems. A recently developed approach, using generalized Langevin equations and phonon Green's functions, is explained and several applications to harmonic systems are given. For interacting systems, various analytic approaches based on the Green–Kubo formula are described, and their predictions are compared with the latest results from simulation. These results indicate that for momentum-conserving systems, transport is anomalous in one and two dimensions, and the thermal conductivity κ diverges with system size L as κ ∼ L α. For one-dimensional interacting systems there is strong numerical evidence for a universal exponent α = 1/3, but there is no exact proof for this so far. A brief discussion of some of the experiments on heat conduction in nanowires and nanotubes is also given.