Statistical analysis of polyatomic quantum beats using the properties of random matrices

We have devised a numerical method of analyzing polyatomic quantum beats for the case when so many states are coherently excited that the properties of individual states are inaccessible. The method involves ensemble averaging singlet character distributions obtained by diagonalization of random matrices and using these distributions in simulations of observable quantum beats. By ensemble averaging the simulated quantum beats, we can correlate, the average parameters which describe the observable fluorescence decays to the molecular parameters that determine the form of the random matrices. We have found that when very complicated quantum beat effects are observed, extra information is available which relates the overall width of the singlet character distribution to a third observable parameter beyond the two parameters that have traditionally been employed to characterize biexponential fluorescence. In the absence of hyperfine structure this method allows the determination of the width of the singlet character distribution even when that width is greater than the width of the excitation source. This is important since our numerical studies also show that the density of nonradiatively coupled states and the root mean square interaction energy determine the width of the distribution of singlet character in a very simple and general fashion. We believe this method can be easily modified to describe other quantum beat phenomena and can presently be used to specify conditions for specific molecules under which quantum beats are observable.