The K-property of Hamiltonian systems with restricted hard ball interactions

Introduction In 1985, Chernov and Sinai suggested the study of a mechanical model of elastic hard balls: the so-called pencase, which we will call the Chernov-Sinai pencase (cf. the manuscript [S-Ch(1985)]). Here large hard ball particles move on a torus, elongated in one spatial dimension; since then the cyclic order of the particles remains invariant, each ball can only interact with its two neighbours. Their idea was that, on one hand, because of the restricted form of the interactions, the expected ergodicity of the model could be easier to establish than that of general hard ball systems on tori and, on the other hand, this quasi-one-dimensional model seems to be a quite suitable mechanical one for the study of the hydrodynamic limit transition (cf. [Sin(1985)]). For systems of elastic hard balls on a torus Yakov Sinai, in 1963, [Sin(1963)] gave a mathematically rigorous version of Boltzmann's celebrated ergodic hypothesis: the system of an arbitrar