ANOMALOUS HEAT CONDUCTION AND ANOMALOUS ENERGY DIFFUSION

Abstract

Heat conduction in low dimensional systems may not follow Fourier's law, which is called anomalous heat conduction. In these thesis, anomalous heat conduction will be discussed from three different aspects.

Firstly, an equality connecting the mean square displacement of energy diffusion and the heat flux autocorrelation function is derived, which connects anomalous heat conduction to anomalous diffusion.

Secondly, a tuning fork method is introduced to study the excited waves in 1D lattices, from which the phonon dispersion relation and mean free paths can be obtained. It is shown that anomalous heat conduction is due to the divergent phonon mean free path in momentum conserving lattices.

Thirdly, Green¿Kubo like formulas for heat fluxes in arbitrarily connected open systems are derived. For 1D anomalous systems, it is shown that heat flux is not a function of the local temperature only, which can even flow against the local temperature gradient.