Characterization of the stretched exponential trap-time distributions in one-dimensional coupled map lattices

Stretched exponential distributions and relaxation responses are encountered in a wide range of physical systems such as glasses, polymers and spin glasses. As found recently, this type of behavior occurs also for the distribution function of certain trap time in a number of coupled dynamical systems. We analyze a one-dimensional mathematical model of coupled chaotic oscillators which reproduces an experimental set-up of coupled diode-resonators and identify the necessary ingredients for stretched exponential distributions.Comment: 8 pages, 8 figure

Relationship between dynamical heterogeneities and stretched exponential relaxation

We identify the dynamical heterogeneities as an essential prerequisite for stretched exponential relaxation in dynamically frustrated systems. This heterogeneity takes the form of ordered domains of finite but diverging lifetime for particles in atomic or molecular systems, or spin states in magnetic materials. At the onset of the dynamical heterogeneity, the distribution of time intervals spent in such domains or traps becomes stretched exponential at long time. We rigorously show that once this is the case, the autocorrelation function of the renewal process formed by these time intervals is also stretched exponential at long time.Comment: 8 pages, 4 figures, submitted to PR