# The relation between stretched-exponential relaxation and the vibrational density of states in glassy disordered systems

## TL;DR

This paper demonstrates that stretched-exponential relaxation in glasses is fundamentally linked to their vibrational density of states, especially soft modes near the glass transition, using a reformulated dielectric response model.

## Contribution

It introduces a generalized Lorentz model connecting dielectric relaxation to vibrational density of states, revealing the origin of stretched-exponential decay in glassy systems.

## Key findings

- Dielectric relaxation near the glass transition follows a stretched-exponential form with Kohlrausch exponents 0.56 to 0.65.
- The relaxation behavior is directly related to soft vibrational modes (boson-peak) in the density of states.
- The model aligns well with experimental observations of dielectric relaxation in glasses.

## Abstract

Amorphous solids or glasses are known to exhibit stretched-exponential decay over broad time intervals in several of their macroscopic observables: intermediate scattering function, dielectric relaxation modulus, time-elastic modulus etc. This behaviour is prominent especially near the glass transition. In this Letter we show, on the example of dielectric relaxation, that stretched-exponential relaxation is intimately related to the peculiar lattice dynamics of glasses. By reformulating the Lorentz model of dielectric matter in a more general form, we express the dielectric response as a function of the vibrational density of states (DOS) for a random assembly of spherical particles interacting harmonically with their nearest-neighbours. Surprisingly we find that near the glass transition for this system (which coincides with the Maxwell rigidity transition), the dielectric relaxation is perfectly consistent with stretched-exponential behaviour with Kohlrausch exponents $0.56 < \beta < 0.65$, which is the range where exponents are measured in most experimental systems. Crucially, the root cause of stretched-exponential relaxation can be traced back to soft modes (boson-peak) in the DOS.