Direct Estimate of the Static Length-Scale Accompanying the Glass Transition

Glasses are liquids whose viscosity has increased so much that they
cannot flow. Accordingly there have been many attempts to define a
static length-scale associated with the dramatic slowing down of
super-cooled liquid with decreasing temperature. In this talk, I will
present a simple method to extract the desired length-scale which is
highly accessible both for experiments and for numerical
simulations. The fundamental new idea is that low lying vibrational
frequencies come in two types, those related to elastic response and
those determined by plastic instabilities. The minimal observed
frequency is determined by one or the other, crossing at a typical
length-scale which is growing with the approach of the glass
transition. This length-scale characterizes the correlated disorder in
the system: on longer length-scales the details of the disorder become
irrelevant, dominated by the Debye model of elastic modes. After
introducing the length-scale I will show how this scale completely
determines the dynamics of the super-cooled liquid under external
constraints, thereby proving beyond doubt the static nature of the
proposed length-scale. Finally I talk about consequence of this scale
on the mechanical properties of the amorphous solids.