  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.
