Fluctuating Phases and Fluctuating Relaxation Times in Glass Forming Liquids

The presence of fluctuating local relaxation times, ${\tau }_r(t)$ has been used for some time as a conceptual tool to describe dynamical heterogeneities in glass-forming systems. However, until now no general method is known to extract the full space and time dependent ${\tau }_r(t)$ from experimental or numerical data. Here we report on a new method for determining the local phase field, ${\varphi }_r(t)={\int }^{t}d{t}^{\mathrm{\prime }}\mathrm{/}{\tau }_r(t^{\mathrm{\prime }})$ from snapshots $\{r(t_i){\}}_{i=\mathrm{1...}M}$ of the positions of the particles in a system, and we apply it to extract ${\varphi }_r(t)$ and ${\tau }_r(t)$ from numerical simulations. By studying how the phase field depends on the number of snapshots, we find that it is a well defined quantity. By studying fluctuations of the phase field, we find that they describe heterogeneities well at long distance scales.