Glass transition in a simple stochasic model with back-reaction

We formulate and solve a model of dynamical arrest in colloids. A particle is coupled to the bath of statistically identical particles. The dynamics is described by Langevin equation with stochastic external force described by telegraphic noise. The interaction with the bath is taken into account self-consistently through the back-reaction mechanism. Dynamically induced glass transition occurs for certain value of the coupling strength. Edwards-Anderson parameter jumps discontinuously at the transition. Another order parameter can be also defined, which vanishes continuously with exponent 1/2 at the critical point. Non-linear response to harmonic perturbation is found.