Heat Transport in low-dimensional systems

TL;DR

This paper reviews theoretical and numerical studies of heat conduction in low-dimensional systems, highlighting anomalous transport behavior and the divergence of thermal conductivity with system size, with some experimental context.

Contribution

It introduces a generalized Langevin and Green's function approach for harmonic systems and compares analytic predictions with simulations for interacting systems, emphasizing anomalous heat transport.

Findings

Thermal conductivity diverges with system size in momentum-conserving systems.

Universal exponent alpha = 1/3 for 1D interacting systems is supported by numerical evidence.

Anomalous heat conduction observed in low-dimensional models and nanostructures.

Abstract

Recent results on theoretical studies of heat conduction in low-dimensional systems are presented. These studies are on simple, yet nontrivial, 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 kappa, diverges with system size L, as kappa ~ L^alpha. For one dimensional interacting systems there is strong numerical evidence for a universal exponent alpha =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.