Femtosecond real-time probing of reactions. XIV. Rydberg states of methyl iodide

The elementary reaction dynamics of methyl iodide in two Rydberg states leading to an iodine and a methyl radical occur on the femtosecond time scale (M.H. Janssen, M. Dantus, H. Guo, and A.H. Zewail. Chem. Phys. Lett. 214, 281 (1993)). In this article, we consider the dynamics of this elementary process which involves both the Rydberg and valence states. Direct comparisons are made between theory and experiment with special focus on the following observations: large isotope effects, mode dependence of the predissociation rates, and coherence effects. The quantal molecular dynamics in two-dimensions show that the initial wave packet motion occurs along a vibrational mode involving the light atoms accompanied by transitions from the Rydberg state to the repulsive state; subsequent dynamics on the dissociative state lead to the C—I bond cleavage. The theoretical calculations also give the decay behavior of the Rydberg states with lifetimes in agreement with those observed in the femtosecond experiments. Moreover, the large isotope effect in observed predissociation rates of CH3I and CD3I has been successfully reproduced by the same model. The two-dimensional dynamics underscore the shortcomings of a one-dimensional picture in which the C—I serves as the sole reaction coordinate. The model presented here offers a viable mechanism for the dynamics of these Rydberg states

Weak expansiveness for actions of sofic groups

In this paper, we shall introduce $h$-expansiveness and asymptotical $h$-expansiveness for actions of sofic groups. By the definitions, each $h$-expansive action of sofic groups is asymptotically $h$-expansive. We show that each expansive action of sofic groups is $h$-expansive, and, for any given asymptotically $h$-expansive action of sofic groups, the entropy function (with respect to measures) is upper semi-continuous and hence the system admits a measure with maximal entropy. Observe that asymptotically $h$-expansive property was firstly introduced and studied by Misiurewicz for $\mathbb{Z}$-actions using the language of topological conditional entropy. And thus in the remaining part of the paper, we shall compare our definitions of weak expansiveness for actions of sofic groups with the definitions given in the same spirit of Misiurewicz's ideas when the group is amenable. It turns out that these two definitions are equivalent in this setting.Comment: to appear in Journal of Functional Analysi