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In order to discern aggregation in solutions, we present a quantum mechanicalanalog of the photon statistics from fluorescent molecules diffusing through afocused beam. A generating functional is developed to fully describe theexperimental physical system as well as the statistics. Histograms of themeasured time delay between photon counts are fit by an analytical solutiondescribing the static as well as diffusing regimes. To determine empiricalfitting parameters, fluorescence correlation spectroscopy is used in parallelto the photon counting. For expedient analysis, we find that the distribution'sdeviation from a single Poisson shows a difference between two single fluormoments or a double fluor aggregate of the same total intensities. Initialstudies were performed on fixed-state aggregates limited to dimerization.However preliminary results on reactive species suggest that the method can beused to characterize any aggregating system.Comment: 30 pages, 5 figure

Discerning aggregation in homogeneous ensembles: A general description of photon counting spectroscopy in diffusing systems