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Structural relaxation is a scale-free process
Structural relaxation is the process via which a liquid explores its
equilibrium ensemble. It is responsible for the dramatic slowing down at
the glass transition, and has thus received a quite considerable amount
of attention. Yet, the mechanisms governing relaxation are still largely
unknown.
We will explore liquid relaxation from the viewpoint that it results
from a series of transitions which are akin to solid-solid
transformations. This idea arises because, at low temperatures, liquids
spend most of the time vibrating around local minima (inherent states,
or ISs) of their potential energy surface. Since inherent states are, by
definition, mechanically stable, they are genuine elastic solids. Hence,
relaxation results from a series of transitions between elastic solids,
and it follows that relaxation events should leave elastic imprints in
the surrounding medium. To support this view, we carry out a systematic
analysis of the statics and dynamics of the inherent stress field
obtained from 2D and 3D numerical simulations.
Our first surprise is that the inherent stress field itself presents
anisotropic and long-ranged (power-law) correlations, which are a clear
indication of elasticity. Moreover, we directly observe that relaxation
events create long-ranged and anisotropic stresses in the surrounding
medium, just like solid-solid transformations. Finally, we can
demonstrate that the relaxation events occurring over finite time
windows are power-law correlated in space. It follows that the
relaxation process is non-local, an observation which comes against the
currently widely held belief that relaxation would decorrelate beyond
some finite length scale. Our work brings evidence that elasticity plays
a crucial role in liquid relaxation.
