Sommaire:

When the motion of particles driven by external forces is restricted by exclusion mechanisms or bottlenecks, non-trivial heterogeneous space-time correlations in their motion may be observed. We studied two examples of such kind of motion, considering two exclusion processes on discrete lattices. The first model is inspired by the slow relaxation occurring when forcing colloidal or granular materials: at high densities increasing the external forcing leads to a strong increase in the viscosity. We explain the blockage dynamics as the coexistence of blocked and mobile regions, arising from a dynamical phase transition. The second model consists in a one-dimensional exclusion process incorporating a localized dynamical defect, inspired by the complexity and richness of mRNA translation. We provide a complete description of the model, characterizing all the possible dynamical regimes and addressing a quantitative explanation of the macroscopic current profiles.

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