Anomalous energy diffusion and heat conduction in one-dimensional system

Abstract

We propose a new concept, the centre of energy, to study energy diffusion and heat conduction in a one-dimensional hard-point model. For the diatom model, we find an anomalous energy diffusion as (x2) ∼ tβ with β = 1.33, which is independent of initial condition and mass rate. The present model can be viewed as the model composed by independent quasi-particles, the centre of energy. In this way, heat current can be calculated. Based on the theory of dynamic billiard, the divergent exponent of heat conductivity is estimated to be α = 0.33, which is confirmed by a simple numerical calculation.