Heat flow through an insulating nanocrystal

We calculate the low temperature, quantum mechanical rate of heat flow through a nanocrystal due to phonon transport by solving a many-body Schrodinger equation for oscillators in Fermi resonance. By analogy to Raman scattering through molecules, we find that normal processes due to anharmonicity of the nanocrystal give rise, over an intermediate range of lengths, to a largely length-independent thermal conductivity that resembles Fourier's law, but is in fact of a different origin. For longer crystals conductivity rises with length, as predicted for a harmonic solid. For shorter nanocrystals thermal conductivity also rises with length, followed by a turnover regime in which thermal conductivity is size specific.