Line shape studies of a state coupled to a random background including large fluctuations of the couplings

Abstract

Line shape functions of a model system are analyzed, describing an oscillator carrying state coupled to background states randomly distributed in energy and with random coupling constants. Depending on the energy distribution functions or the nature of the coupling distribution, different line shape functions, such as the Lorentzian, the Fano, or that related to the nonexponential decay of the Forster type are recovered as limiting cases. Conditions for the range of applicability of a specially introduced mean square coupling approximation are derived. It is shown that the appearance of a Lorentzian line shape does not imply directly a homogeneous decay mechanism and that, on the other hand, commonly accepted conditions for the so-called statistical limit, expressed in terms of an average density and an average coupling, do not necessarily lead to a Lorentzian line shape. This is illustrated analytically through a model with randomly distributed transition dipolar couplings. Other applications relate to spectral diffusion in proteins and to bridged charge transfer.