Fluctuating Phases and Fluctuating Relaxation Times in Glass Forming Liquids

The presence of fluctuating local relaxation times, $τ_r(t)$ 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 $τ_r(t)$ from experimental or numerical data. Here we report on a new method for determining the local phase field, $φ_r(t) = ∫^t dt'/τ_r(t')$ from snapshots ${r(t_i)}_i=1...M$ of the positions of the particles in a system, and we apply it to extract $φ_r(t)$ and $τ_r(t)$ 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.