Moment-Preserving Theory of Vibrational Dynamics of Topologically Disordered Systems

Frontiers in Physics

Folli, Viola¹  Ruocco, Giancarlo¹  Schirmacher, Walter² 

[1] Center for Life Nano Science, Fondazione Istituto Italiano di Tecnologia, Rome, Italy;Department of Physics, University of Rome ‘La Sapienza’, Rome, Italy

关键词: glasses;    disordered systems;    vibrational dynamics;    Density of States;    Theory;    SCBA;    Heterogeneous elasticity;   

DOI  :  10.3389/fphy.2017.00029

学科分类：物理（综合）

来源: Frontiers

【 摘 要 】

We investigate a class of simple mass-spring models for the vibrational dynamics of topologically disordered solids. The dynamical matrix of these systems corresponds to the Euclidean-RandomMatrix (ERM) scheme. We show that the self-consistent ERM approximation introduced by Ganter and Schirmacher, Phys. Rev. B82, 094205 (2010) preserves the first two nontrivial moments of the level density exactly. We further establish a link between these approximations and the fluctuating elasticity approaches. Using this correspondence we derive and solve a new, simplified mean-field theory for calculating the vibrational spectrum of disordered mass-spring models with topological disorder. We calculate and discuss the level density and the spectral moments for a model in which the force constants obey a Gaussian site-separation dependence. We find fair agreement between the results of the new theory and a numerical simulation of the model. For systems with finite size we find that the moments strongly depend on the number of sites, which poses a caveat for extrapolating finite-system simulations to the infinite-size limit.

【 授权许可】

CC BY