On the use of antithetic variates in particle transport problems

The possible use of antithetic variates as a method of variance reduction in particle trans- port problems is investigated, by performing some numerical experiments. It is found that if variance reduction is not very carefully de®ned, it is possible, with antithetic variates, to spuriously detect reduction, or not detect true reduction. Once such subtleties are overcome, it is shown that antithetic variates can reduce variance in multidimensional integration up to a point. The phenomenon of spontaneous correlation is de®ned and identi®ed as the cause of failure. The surprising result that it sometimes pays to track non-contributing particle his- tories is demonstrated by means of a zero variance integration analogue. The principles developed in the investigation of multi-variable integration are then employed in a simple calculation of energy deposition using the EGS4 computer code. Promising results are obtained for the total energy deposition problem, but the depth/dose problem remains unsolved. Possible means of overcoming the diculties are suggested.