Title: Glassy dynamics on the sphere
Abstract:
We studied a model based on a simple ingredient in order to describe
the dynamics of a supercooled liquid. Starting from a monodisperse
Lennard-Jones system on the euclidean plane, we added frustration by
curving the space to form a sphere of arbitrary radius.
Using a molecular dynamics algorithm, we showed that this system
indeed behaves like a glassy liquid.
The dynamics, caracterized by the self-intermediate scattering
function Fs(k,t), slows down strongly and changes shape at low
temperature, for a small variation of the statics, which we tried
to explain theoretically through the study of the mode coupling
theory (MCT) on the sphere.
We derived the dynamical equation of spherical MCT and studied the
long time limit of its solution. The spherical MCT predicts a dynamic
transition similar to the one predicted by euclidean MCT, which does
not allow us to explain the effect of curvature on Fs(k,t), though the
curvature has an influence on the value of the transition temperature.
Finally, we took interest in the role of "defects", among which a
minimal number of 12 is imposed by topology. At low temperature, the
defects tend to form linear structures, which is predicted
theoretically and observed in some experiments. The defects have a
strong contribution in the relaxation, but the role of other particles
is however not negligible.