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We study diffusion on a periodic billiard table with infinite horizon in thelimit of narrow corridors. An effective trapping mechanism emerges according towhich the process can be modeled by a L\'evy walk combiningexponentially-distributed trapping times with free propagation along pathswhose precise probabilities we compute. This description yields anapproximation of the mean squared displacement of infinite-horizon billiards interms of two transport coefficients which generalizes to this anomalous regimethe Machta-Zwanzig approximation of normal diffusion in finite-horizonbilliards [Phys. Rev. Lett. 50, 1959 (1983)].

Machta-Zwanzig regime of anomalous diffusion in infinite-horizon billiards