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While multiple time scales generally arise in the dynamics of disordered systems, we find multiple time scales in absence of disorder, in a simple model with hard local constraints. The dynamics of the model, which consists of local collective rearrangements of various scales, is not determined by the smallest scale but by a length $l^*$ that grows at low energies. In real space we find a hierarchy of fast and slow regions: each slow region is geometrically insulated from all faster degrees of freedom, which are localized in fast pockets below percolation thresholds. A tentative analogy with structural glasses is given, which attributes the slowing down of the dynamics to the growing size of mobile elementary excitations, rather than to the size of some domains.
We investigate the statistics of encounters of a diffusing particle with different subsets of the boundary of a confining domain. The encounters with each subset are characterized by the boundary local time on that subset. We extend a recently propos
Diffusive dynamics in presence of deep energy minima and weak nongradient forces can be coarse-grained into a mesoscopic jump process over the various basins of attraction. Combining standard weak-noise results with a path integral expansion around e
Brownian motion has played important roles in many different fields of science since its origin was first explained by Albert Einstein in 1905. Einsteins theory of Brownian motion, however, is only applicable at long time scales. At short time scales
A system of hard spheres exhibits physics that is controlled only by their density. This comes about because the interaction energy is either infinite or zero, so all allowed configurations have exactly the same energy. The low density phase is liqui
By considering the constrained motion of classical spins in a geometrically frustrated magnet, we find a dynamical freezing temperature below which the system gets trapped in metastable states with a frozen moment and dynamical heterogeneities. The r