Abstract
An ergodic theoretic basis for the statistical theory of isomerization is provided. A strong mixing assumption is used to derive the absorbing boundary method of computing isomerization dynamics. In addition, the absorbing boundary method is shown to fail in systems exhibiting certain long-time correlations. In order to account for these correlations, we construct a new statistical theory termed the ‘‘flux renewal model.’’ The new model is based on the consistent application of strong mixing, with the incorporation of nonzero relaxation time. It utilizes statistical calculations to eliminate the explicit computation of long-time trajectories exhibiting characteristics of chaos. The flux renewal model is tested and compared with the absorbing boundary method via numerical computations of the isomerization dynamics of the chaotic siamese stadium billiard. The flux renewal model is shown to give the best approximation to the isomerization flux–flux correlation. It does this by simultaneously handling nonstatistical correlations and long-time scale exponential decay. In addition, with less computational effort, the flux renewal model generally provides more accurate rate constant estimates than the absorbing boundary method.
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