# Local Density Fluctuation Governs the Divergence of Viscosity underlying Elastic and Hydrodynamic Anomalies in a 2D Glass-Forming Liquid

## TL;DR

This paper demonstrates that in a 2D glass-forming liquid, local density fluctuations govern the divergence of viscosity, linking microscopic relaxation to macroscopic flow properties, with long-wavelength fluctuations playing a crucial role.

## Contribution

It reveals that relative particle displacement correlates with viscosity growth and highlights the impact of elastic and hydrodynamic fluctuations on long-wavelength dynamics in 2D glasses.

## Key findings

- Relaxation time scales with viscosity.
- Long-wavelength fluctuations cause logarithmic divergence in diffusivity.
- Hydrodynamic fluctuations significantly influence 2D glass dynamics.

## Abstract

If a liquid is cooled rapidly to form a glass, its structural relaxation becomes retarded, producing a drastic increase in viscosity. In two dimensions, strong long-wavelength fluctuations persist, even at low temperature, making it difficult to evaluate the microscopic structural relaxation time. This Letter shows that, in a 2D glass-forming liquid, relative displacement between neighbor particles yields a relaxation time that grows in proportion to the viscosity. In addition to thermal elastic vibrations, hydrodynamic fluctuations are found to affect the long-wavelength dynamics, yielding a logarithmically diverging diffusivity in the long-time limit.