Billiards correlation functions | Zendy

Pedro L. Garrido | Zendy; Giovanni Gallavotti | Zendy

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Billiards correlation functions

Author(s) -

Pedro L. Garrido,

Giovanni Gallavotti

Publication year - 1994

Publication title -

journal of statistical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.71

H-Index - 115

eISSN - 1572-9613

pISSN - 0022-4715

DOI - 10.1007/bf02188675

Subject(s) - dynamical billiards , autocorrelation , mixing (physics) , exponential function , statistical physics , mathematics , exponential decay , classical mechanics , physics , mathematical analysis , quantum mechanics , geometry , statistics

We discuss various experiments on the time decay of velocityautocorrelation functions in billiards. We perform new experiments andfind results which are compatible with an exponential mixinghypothesis, first put forward by Friedman and Martin, [FM]: they donot seem compatible with the stretched exponentials believed, in spiteof [FM] and more recently of Chernov, [C], to describe the mixing. Theanalysis led us to several byproducts: we obtain information about thenormal diffusive nature of the motion and we consider the probabilitydistribution of the number of collisions in time tm (as t\to\infty$)finding a strong dependence on some geometric characteristics of thelocus of the billiards obstacles

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