Open AccessApplication of the random matrix theory to vibrational properties of amorphous solids
Author(s) -
D. A. Conyuh,
Y. M. Beltukov
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1391/1/012118
Subject(s) - amorphous solid , random matrix , matrix (chemical analysis) , physics , thermodynamics , materials science , chemistry , crystallography , quantum mechanics , eigenvalues and eigenvectors , composite material
In this work, we apply the random matrix theory to the study of vibrational properties of disordered systems with a big number of degrees of freedom, such as amorphous solids. Mechanical stability of amorphous solids implies the Wishart ensemble with the positive definite dynamical matrix of the form M ^ = B ^ B ^ T . The translational invariance in amorphous solids leads to the sum rule Σ i B ij = 0, which means non-zero correlations of the matrix elements B ij . The proposed correlated Wishart ensemble has many universal properties of amorphous solids. One of these properties is the boson peak in the reduced vibrational density of states g ( ω ) ω 2 . The boson peak has been observed in many experiments on amorphous solids, but its nature was not clear so far. We show that the boson peak naturally occurs in the proposed model and find its analytical form.