Anomalous Heat Diffusion

Abstract

Consider anomalous energy spread in solid phases, i.e., $MSD=\int (x-{<x>}_E{)}^2{\rho }_E(x,t)dx\propto t^{\beta }$, 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 $C_{JJ}(t)$ is shown to obey rigorously the intriguing relation, $d^{2}MSD/d{t}^2=2C_{JJ}(t)/(k_B{T}^{2}c)$, where $c$ is the specific volumetric heat capacity. Its integral assumes a time-local Helfand-moment relation; i.e. $dMSD/dt{|}_{t=t_s}=2/(k_B{T}^{2}c){\int }_0^{t_s}{C}_{JJ}(s)ds$, 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.

This paper has been withdrawn by the authors. This arXiv article is now the improved and amended version of arXiv:1103.2835v4

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