Physics – Condensed Matter – Statistical Mechanics
Scientific paper
1998-12-10
Jpn. J. Appl. Phys. Vol. 39(2000) Part 1, No. 3A, 1442-1456.
Physics
Condensed Matter
Statistical Mechanics
26 pages,13 figures, typos in appendix A corrected, and title slightly changed
Scientific paper
It is shown that superefficient Monte Carlo computations can be carried out by using chaotic dynamical systems as non-uniform random-number generators. Here superefficiency means that the expectation value of the square of the error decreases to 0 as 1/N^{2} with N successive observations for N-> infinity, whereas the conventional Monte Carlo simulation gives the square of the error in the order 1/N. The order of N in the error convergence speed of superefficient Monte Carlo computations does not depend on the dimensionality of the problems. By deriving a necessary and sufficient condition for the superefficiency, it is shown that such high-performance Monte Carlo simulations can be carried out only if there exists a strong correlation of chaotic dynamical variables.
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