Anosov C-systems and random number generators

Abstract

We are developing further our earlier suggestion to use hyperbolic Anosov C-systems for the Monte-Carlo simulations in high energy particle physics. The hyperbolic dynamical systems have homogeneous instability of all trajectories and as such they have mixing of all orders, countable Lebesgue spectrum and positive Kolmogorov entropy. These extraordinary ergodic properties follow from the C-condition introduced by Anosov. The C-condition defines a rich class of dynamical systems which span an open set in the space of all dynamical systems. The important property of C-systems is that they have a countable set of everywhere dense periodic trajectories and that their density exponentially increases with entropy. Of special interest are C-systems that are defined on a high dimensional torus. The C-systems on a torus are perfect candidates to be used for Monte-Carlo simulations. Recently an efficient algorithm was found, which allows very fast generation of long trajectories of the C-systems. These trajectories have high quality statistical properties and we are suggesting to use them for the QCD lattice simulations and at high energy particle physics.