Glass transition induced by the spatially correlated stochastic dynamics.

The colloidal glass transition, i.e. the extreme rise in the viscosity that causes the jamming of the disordered systems, remains a challenging problem in the soft-matter theory. In particular, the glassy systems are characterized by the presence of significant spatial correlations in the molecular dynamics. In this letter we report on the exactly solvable model that provides a new insight into the role of these correlations i.e. it shows that their presence is the necessary conditions for the jamming to occur. These results suggest that the process of correlations growth might be microscopically decoupled from the mechanism behind the jamming. The model is one-dimensional, mesoscopic and admits arbitrary interactions between particles. It stems from the framework of collective diffusion, i.e. the recently introduced Langevin dynamics with spatially correlated noise and friction-response matrix. We show that the mechanism of singular dissipation is embedded in this matrix and we find that the spectrum of this matrix acts as the order parameter for glass transition. The critical parameters predicted with this model qualitatively agree with the experimental values.