Heat transport in low-dimensional systems

• Published in: Advances in physics Vol. 57; no. 5; pp. 457 - 537
• Main Author: Dhar, Abhishek
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 01.09.2008; Taylor & Francis
• Subjects: anomalous transport; Condensed matter: structure, mechanical and thermal properties; Exact sciences and technology; heat conduction; Lattice dynamics; low-dimensional systems; Nonelectronic thermal conduction and heat-pulse propagation in solids; thermal waves; Phonons in low-dimensional structures and small particles; Physics; Transport properties of condensed matter (nonelectronic); Phononic crystal; Two-dimensional systems; Kubo formula; Mode coupling; Nanotubes; Momentum; Langevin equation; Lattice model; Hydrodynamic model; Thermal conductivity; Nanowires; Green's function methods; One-dimensional systems
• ISSN: 0001-8732; 1460-6976
• DOI: 10.1080/00018730802538522

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.