A numerical study of the thermal conductivity in amorphous systems

Transport properties of vibrations play a crucial role in thermal conductivity of amorphous dielectrics and semiconductors. In the present paper, we use numerical methods to analyze the vibrational properties. We propose a modification of the Kernel Polynomial Method (KPM) to calculate vibrational density of states and diffusivity of the vibrational energy. It is shown that the proposed method is more efficient for big amorphous systems than the full diagonalization of the dynamical matrix. The main recurrence relation is similar to the Verlet integration, which allows to use the analogy with the time evolution.