Dynamical transition on the periodic Lorentz gas: Stochastic and deterministic approaches.

The effect of dynamical properties of the periodic Lorentz gas on the autocorrelation function and diffusion coefficient are investigated in various geometric transitions between billiards without horizon and infinite horizon. Numerical simulations are performed using a double square lattice which permits us to isolate different types of corridors and to describe the individual effects of each corridor. The results are compared with a stochastic model based on a escape-rate formalism which reveals the sensibility of the diffusion coefficient and clarifies the role of the open corridors mechanism on the dynamical transitions.