Stochastic models for heterogeneous relaxation: application to inhomogeneous optical lineshapes

Abstract

Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale. Starting from the most simple Gaussian Markov process we model the exchange between 'slow' and 'fast' environments by treating the fluctuating single-particle variable as a projection from a higher-dimensional Markov process. The moments of the resulting stochastic process are calculated from the corresponding Master equations or Langevin equations, depending on the model. The calculations show the importance of the way to treat exchange processes. The resulting stochastic process is non-Markovian for all models. However, the deviations from a Gaussian behavior depend on the details of the models. A comparison of our results with other model treatments and experiments should provide further insight into the concept of dynamic heterogeneity.

Kerr effect as a tool for the investigation of dynamic heterogeneities

“…( 12). This also holds in other exchange models [24]. Large exchange rates thus lead to a weaker L-dependence of the eigenvalues, and the exponents in correlation functions (13) for different values of L become more and more similar.…”

“…Finite life times can be modelled via exchange models. Various approaches exist to include exchange in a model [24]. In a master equation ansatz [25] one assumes that slow environments become fast and vice versa.…”

Persistence in a Simple Model for the Earth's Atmosphere Temperature Fluctuations

“…A study of the presented model in the context of general systems with several time scales is also intended. The study of such systems is important in fields like control theory, inhomogeneous media and predator-pray systems among others [1,2,3,4,5].…”

“…Interaction among processes with several length and time scales is common to a variety of complex systems. For instance, the long-range temporal correlations found in signals from a variety of fields can be associated with an interplay of a number of time scales [1,2,3,4,5]. In particular, it is an extended belief that the persistence observed in the temperature fluctuations of the Earth's atmosphere is a consequence of its feedback with slower dynamical components in the climate system, like the oceans and Earth's surface [3].…”

“…(1) are calculated by averaging over a year and over the entire Earth's surface. Assuming a blackbody process, the average atmosphere's temperature is given by y = νT 4 , where ν is the Stefan-Boltzmann constant. In spite of its simplicity, the zero dimensional energy balance model is capable of predicting with very good accuracy the mean Earth's surface temperature.…”