Kinetically drivenglassy transition in an exactly solvable toy model witha reversible mode coupling mechanism and trivial statics

Abstract

We propose a toy model with a reversible mode coupling mechanismand with a trivial Hamiltonian (and hence trivial statics). Themodel can be analysed exactly without relying upon uncontrolledapproximation such as the factorization approximation employedin the current mode coupling theory. We show that the model exhibits akinetically driven transition from an ergodic phase to a nonergodic phase. The nonergodic state is the nonequilibriumstationary solution of the Fokker-Planck equation for thedistribution function of the model.