Z. Shemer | Searcharxiv

arXiv2006

Correlated weak bonds as a source of the Boson peak in glasses

Many attempts to explain the Boson peak in the vibrational spectra of glasses consider models of a lattice of harmonic oscillators connected by spring constants of varying strength and randomly distributed. However, in real glasses one expects that some molecules will be connected to their neighbors by more than one weak bond, so that a realistic model should consider oscillators with several weak springs. In this paper, a t-matrix formalism is used to study the effect of such correlated weak springs in a scalar model on a simple cubic lattice with a binary distribution of spring constants. Our results, which are confirmed by computer simulations, show that a concentration of c oscillators with z weak springs and 6-z strong ones leads to a low frequency peak in the reduced density of states (Boson peak) even when the total concentration of weak springs cz is less than 10%., No such peak has been found at these low concentrations in previously reported calculations which used effective medium methods. For a given value of cz, this peak becomes more pronounced and moves to much lower frequencies as z increases.

cond-mat.dis-nn↗

arXiv2005

A new approach to strongly correlated disorder

Problems involving disordered systems are usually analyzed for systems with random disorder. However, there are many systems in which the main disorder involves clusters with correlated differences between their properties and those of the average system. A new approximation, the average trace approximation, is proposed for calculating the diagonal elements of the Green function, and hence the density of states, in such systems. As an example, application of the method to a simple cubic array of harmonic oscillators shows that correlation in the disorder leads to a peak in the low frequency density of states, a result confirmed by computer simulations.

cond-mat.dis-nn↗