Canonical superdiffusion and energy fluctuation divergence

We propose a noble physical model obtained from a Hamiltonian with periodic potential. This model is canonical, reversible and brings about chaotic superdiffusion with energy fluctuation divergence. The analytical formula of invariant density can be obtained in some parameter range. In the range it is proved that the map is Anosov diffeomorphism and the invariant measure is a SRB measure. We calculate the analytical formula of Lyapunov exponent.