## Anomalous Heat Diffusion    [PDF]

Sha Liu, Peter Hänggi, Nianbei Li, Jie Ren, Baowen Li
Consider anomalous energy spread in solid phases, i.e., $MSD= \int (x -{\langle x \rangle}_E)^2 \rho_E(x,t)dx \propto t^{\beta}$, as induced by a small initial excess energy perturbation distribution $\rho_{E}(x,t=0)$ away from equilibrium. The associated total thermal equilibrium heat flux autocorrelation function $\Corr_{JJ}(t)$ is shown to obey rigorously the intriguing relation, $d^2 MSD/dt^2 = 2\Corr_{JJ}(t)/(k_BT^2c)$, where $c$ is the specific volumetric heat capacity. Its integral assumes a time-local Helfand-moment relation; i.e. $d\msd/dt|_{t=t_s} = 2/(k_BT^2c)\int_0^{t_s} \Corr_{JJ}(s)ds$, where the chosen cut-off time $t_s$ is determined by the maximal signal velocity for heat transfer. Given the premise that the averaged nonequilibrium heat flux is governed by an anomalous heat conductivity, energy diffusion scaling necessarily determines a corresponding anomalous thermal conductivity scaling behavior.
View original: http://arxiv.org/abs/1306.3167