MIXMAX · Development and Implementation of new generation of Pseudo Random Number Generators based on Kolmogorov-Anosov K-systems

Development and Implementation of new generation of Pseudo Random Number Generators based on Kolmogorov-Anosov K-systems

Modern powerful computers open a new era for the application of the Monte Carlo Method for the simulation of physical systems with many degrees of freedom and of higher complexity. The Monte Carlo simulations are important computational techniques in many areas of natural sciences and have significant application in particle and nuclear physics, quantum physics, statistical physics, quantum chemistry, material science, among many other multidisciplinary applications. In the heart of the Monte Carlo simulations are Pseudo Random Number Generators (PRNG). The primary objective of the MIXMAX project is a systematic development and implementation of the state of the art new generation of Pseudo Random Number Generators based on Kolmogorov-Anosov C-K systems, which demonstrates excellent statistical properties, into a multidisciplinary usable product. This innovative class of MIXMAX PRNGs was proposed earlier by the members of the network and relies on the fundamental discoveries and results of Ergodic theory. The MIXMAX generator is a fast generator and has exceptional statistical properties. As a fast and high quality generator the MIXMAX will allow to save financial and energy resources in science, research and industry spent for the massive Monte-Carlo simulations in the fields of high energy physics, biophysics, chemistry, Earth and environment, plasma physics, fluid dynamics, molecular structures and development of new materials. A saving of energy consumption by large computing facilities and cooling systems damping the hot water into the river and of the hot air, would be possible with a more efficient Monte Carlo simulations based on MIXMAX generators. The new approach to generate pseudo random numbers can provide a solution for vastly needed high entropy random number generators for communication systems. The overall objectives of the MIXMAX network is to turn these ideas and earlier research on C-K systems generators into a usable product, to develop an efficient program of the C-K system generator with tuneable internal parameters of maximal dimensionality and of the order of the Galois field, embedded into a user friendly environment, to provide statistical data representing internal characteristics of the C-K-system generator, to implement the C-K system generators into the concurrent and distributed software at CERN for applications in LHC and other HEP experiments, to perform large scale simulations in Quantum Gravity and Quantum Field Theory, to disseminate the product at CERN and other research centres.

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