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 systems (TLSs). Depending on their random environment, SMs exhibit a wide variety of behaviors. Under certain conditions, given in the text, line shapes exhibit simple behavior, e.g., cases where lines are Lorentzian with a width which varies from one molecule to the other. As control parameters are changed a transition to complex line shape phenomena is observed (i.e., the line 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 identical though randomly distributed in space and (ii) the standard tunneling model of low temperature glass where the TLSs are nonidentical. We show that, 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 distribution of linewidth measured in experiment are related. For the line shape problem of SMs in glass we show that background TLSs, defined in the text, can be treated collectively using a simple Gaussian approximations. The Gaussian approximation for the background reduces the number of TLSs needed for a full size simulation of the SM glass system. (C) 2000 American Institute of Physics. [S0021-9606(00)51735-8].