Transition from simple to complex behavior of single molecule line shapes in disordered condensed phase

We use the Kubo-Anderson sudden jump approach to investigate line shapes of single molecules (SMs) interacting with randomly distributed two level sys tems (TLSs). Depending on their random environment, SMs exhibit a wide vari ety of behaviors. Under certain conditions, given in the text, line shapes exhibit simple behavior, e.g., cases where lines are Lorentzian with a widt h which varies from one molecule to the other. As control parameters are ch anged a transition to complex line shape phenomena is observed (i.e., the l ine shapes have random structures, each with a random number of peaks). We investigate these behaviors for two cases-(i) the case when all TLSs are id entical though randomly distributed in space and (ii) the standard tunnelin g model of low temperature glass where the TLSs are nonidentical. We show t hat, in certain limits, both models can be analyzed using Levy-stable laws. For the glass model we compute the distribution of line shape variance and discuss a previous proposition, that distribution of variance and the dist ribution of linewidth measured in experiment are related. For the line shap e problem of SMs in glass we show that background TLSs, defined in the text , can be treated collectively using a simple Gaussian approximations. The G aussian approximation for the background reduces the number of TLSs needed for a full size simulation of the SM glass system. (C) 2000 American Instit ute of Physics. [S0021-9606(00)51735-8].