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We consider a Sinai billiard where the usual hard disk scatterer is replacedby a repulsive potential with $V(r)\sim\lambda r^{-\alpha}$ close to theorigin. Using periodic orbit theory and numerical evidence we show that itsspectral statistics tends to Poisson statistics for large energies when$\alpha<2$ and to Wigner-Dyson statistics when $\alpha>2$, while for $\alpha=2$it is independent of energy, but depends on $\lambda$. We apply the approach ofAltshuler and Levitov [Phys. Rep. {\bf 288}, 487 (1997)] to show that thetransition in the spectral statistics is accompanied by a dynamicallocalization-delocalization transition. This behaviour is reminiscent of ametal-insulator transition in disordered electronic systems.Comment: 8 pages, 2 figures, accepted for publication in Phys. Rev. Let

Spectral Statistics and Dynamical Localization: Sharp Transition in a Generalized Sinai Billiard