Abstract

Molecular dynamics and Monte Carlo simulations are important computational techniques in many areas of science: in quantum physics [1], statistical physics [2], nuclear physics [3], quantum chemistry [4], material science [5], among many others. The simulations rely heavily on the use of random numbers, which are generated by deterministic recursive rules. Such rules produce pseudo random numbers, and it is a great challenge to design random number generators (RNG) that behave as realizations of independent uniformly distributed random variables and approximate “true randomness”[6].
There are several requirements for a good RNG and its implementation in a subroutine library. Among them are statistical robustness (uniform distribution of values at the output with no correlations), unpredictability, long period length, efficiency, theoretical support (precise prediction of the important properties), portability and others [6, 7, 8]. A number of RNGs introduced last five decades fulfill most of the requirements and are successfully employed in simulations. Nevertheless, each of them have some weak properties which may (or may not) influence the results. The most widely used RNGs can be divided into two classes. The first class is represented by the Linear Congruential Generator (LCG), and the second, by Shift Register (SR) generator. Linear Congruential Generators (LCG) are the best-known and (still) most widely available RNGs in use today. An example of the realization of an LCG generator is the UNIX rand generator yn=(1103515245 yn− 1+ 12345)(mod 231). The practical recommendation is that LCGs should be avoided for …

Date

2004

Authors

L Barash, LN Shchur

Journal

arXiv preprint physics/0409069