| Abstract
| - Single molecule spectroscopy in disordered lattice is investigated from a theoretical point of view. We considerenergy fluctuations of the molecule due to dipolar interactions with two level system (TLS) defects distributedrandomly on a three-dimensional cubic lattice. Each independent TLS is randomly flipping so the energy ofthe molecule is time dependent. We investigate the probability distribution g(W) of the variance of the energyfluctuations. The exact solution, found for finite systems, exhibits peaks, peaks within peaks, etc., correspondingto interaction with nearest neighbors, next-nearest neighbors, etc. For an infinite crystal at high defect density,the distribution of W is shown to depend strongly on the interaction with nearest neighbors and hence onlattice symmetry. At low defect density, g(W) exhibits several peaks separated by large gaps in which g(W)∼ 0. We explain these peaks in terms of contributions from single defects located on discrete distances fromthe molecule. For the continuum version of our model, g(W) is a Lévy stable nonsymmetrical probabilitydensity function, decaying according to g(W) ∼ W-3/2. We discuss the relation between the continuum andlattice models.
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