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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 1: Statistische Mechanik

MP 1.3: Vortrag

Dienstag, 17. März 2015, 10:10–10:30, HFT-FT 101

Random-matrix theory of phonon density of states in disordered solids — •Rico Milkus and Alessio Zaccone — Physics Department, Technische Universität München

The dynamical (Hessian) matrix of solids provides access to the thermal properties of materials, and to the vibrational phonon spectrum (density of states). In ordered crystalline lattices, the lattice periodicity allows for analytical diagonalization in reciprocal space owing to the periodicity and translational-rotational invariance of the lattice. With disordered solids, which lack periodicity, diagonalization can be done only numerically, in real space. We present a new numerical protocol to study the eigenmodes and phonon spectrum of continuous random networks, a realistic model for many amorphous materials. It is shown that the part of the spectrum controlled by randomness, which gives rise to the non-Debye boson peak in the density of states, cannot be described by analytical mean-field models. Yet analytical scaling laws can be extracted, and an analytic representation of the phonon spectrum can be obtained using random matrix theoretical tools. Our results clearly indicate that the origin of the non-Debye boson-peak anomaly in the spectrum is due to the interplay between phonon scattering by the randomness and non-affine elastic response related to connectivity of the network.