Abstract
It is well known that various amorphous solids have many universal properties. One of them is the temperature dependence of the thermal conductivity. However, the microscopic mechanism of the heat transfer above 20 K is still poorly understood. Recent numerical simulations of amorphous silicon and silica show that vibrational modes in the corresponding frequency range (above several THz) are delocalized, however they are completely different from low-frequency acoustic phonons, called “diffusons”.In this work we present a stable random matrix model of an amorphous solid. In this model one can vary the strength of disorder going from a perfect crystal to extremely disordered soft medium without macroscopic rigidity. We show that real amorphous solids are close to the second limiting case, and that diffusons occupy the dominant part of the vibrational spectrum. The crossover frequency between acoustic phonons and diffusons is determined by the Ioffe-Regel criterion. Interestingly, this crossover frequency practically coincides with the Boson peak position. We also show that, as a function of frequency, the diffusivity and the vibrational density of states of diffusons are practically constant. As a result, the thermal conductivity is a linear function of temperature up to rather high temperatures and then saturates. This conclusion is in agreement with numerous experimental data.Further, we consider a numerical model of amorphous silicon-like materials and investigate the role of disorder for longitudinal and transverse vibrations. We also show that the random matrix theory can be successfully applied to estimate the vibrational density of states of granular jammed systems.