Non-periodic pseudo-random numbers used in Monte Carlo calculations

TL;DR

This paper introduces a method for generating non-periodic pseudo-random numbers using the logistic map, demonstrating their effectiveness and potential applications in Monte Carlo simulations, cryptography, and quantum computing.

Contribution

It presents a simple chaotic system-based pseudo-random number generator that is non-periodic up to 10^{13} numbers and suitable for various computational applications.

Findings

Numbers are non-periodic up to 10^{13} generated.

Generated numbers show no correlation.

Applicable to Monte Carlo, cryptography, and quantum simulations.

Abstract

The generation of pseudo-random numbers is one of the interesting problems in Monte Carlo simulations, mostly because the common computer generators produce periodic numbers. We used simple pseudo-random numbers generated with the simplest chaotic system, the logistic map, with excellent results. The numbers generated in this way are non-periodic, which we demonstrated for 10$^{13}$ numbers, and they are obtained in a deterministic way, which allows to repeat systematically any calculation. The Monte Carlo calculations are the ideal field to apply these numbers, and we did it for simple and more elaborated cases. Chemistry and Information Technology use this kind of simulations, and the application of this numbers to Quantum Monte Carlo and Cryptography is immediate. I present here the techniques to calculate, analyze and use these pseudo-random numbers, show that they lack periodicity up to 10$^{13}$ numbers and that they are not correlated.