Non-periodic Pseudo-random Numbers Used In Monte Carlo Calculations

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 1013 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 1013 numbers and that they are not correlated. © 2007 Elsevier B.V. All rights reserved.3982468471Collins, J.J., (1992) Comput. Phys., 6, p. 630Gonzalez, J.A., Reyes, L.I., Guerrero, L.E., (2001) Chaos, 11, p. 1James, F., (1995) Chaos Solitons Fractals, 6, p. 221Onsager, L., (1944) Phys. Rev., 65, p. 117Ferrenberg, A.M., Landau, D.P., (1991) Phys. Rev. B, 44, p. 5081Press, W.H., Teukoisky, S.A., Vetterling, W.T., Flannery, B.B., (1995) Numerical Recipes in C, , Cambridge University Press, Cambridge, MAMetropolis, N., Rosenbluth, A.W., Teller, A.M., Teller, E., (1953) J. Chem. Phys., 21, p. 108