title: Anomalous heat conduction and anomalous diffusion in one-dimensional systems.
abstract: We establish a connection between anomalous heat conduction and anomalous diffusion in one-dimensional systems. It is shown that if the mean square of the displacement of the particle is <Deltax(2)>=2Dt(alpha)(0<alpha</=2), then the thermal conductivity can be expressed in terms of the system size L as kappa=cL(beta) with beta=2-2/alpha. This result predicts that normal diffusion (alpha=1) implies normal heat conduction obeying the Fourier law (beta=0) and that superdiffusion (alpha>1) implies anomalous heat conduction with a divergent thermal conductivity (beta>0). More interestingly, subdiffusion (alpha<1) implies anomalous heat conduction with a convergent thermal conductivity (beta<0), and, consequently, the system is a thermal insulator in the thermodynamic limit. Existing numerical data support our results.
authors.affiliation: Department of Physics, National University of Singapore, Singapore 117542, Republic of Singapore.
authors.forename: Baowen
authors.initials: B
authors.lastname: Li
authors.forename: Jiao
authors.initials: J
authors.lastname: Wang