Energy Transport of Jammed Systems*

We performed computer simulations to calculate the thermal diffusivity of vibrational modes in jammed sphere packings near the jamming transition (Point J). The diffusivity $d(\omega)$ is low for all modes, including those at low frequency $\omega$, and appears to be finite in the zero frequency limit. In ordinary solids, by contrast, $d(\omega)$ diverges at low frequencies due to long wavelength plane waves. The low- frequency modes near Point J are very different from plane waves: they are quasi-localized with large anharmonic corrections. Thus, these modes, which can be viewed as harmonic precursors to two-level systems, are poor conductors of energy.