Thermal conductance and giant fluctuations in one-dimensional disordered systems

The thermal conductance for the energy transport through a disordered harmonic chain is calculated by a tunneling expression of the energy current. The dominant contribution comes from quasiballistic phonons for which the localization length is comparable to the size of the chain. A universal regime of conductance in $k_B^2$T/ħ is obtained at low temperature, while giant fluctuations are predicted at higher temperature. Analogies with electrical conductance are established and conditions for measurements are discussed.