Slow stretched-exponential and fast compressed-exponential relaxation from local event dynamics

Stretched Exponential Relaxation

2 Stretched exponential relaxation in glassy systems 2 2.1 Mathematical properties of the stretched exponential . . . . . . . . . . . . . . . . 3 2.1.1 τ distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.2 Behavior near zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.3 Properties of G(k)/G(τ) . . . . . . . . . . . . . . . . . . . . ....

Stretched Exponential Relaxation and Independent Relaxation Modes

We discuss the origin of stretched exponential relaxation in disordered Ising spin systems by writing the master equation on the phase space, and the evolution of local and global spin autocorrelation functions, in terms of independent relaxation modes, which are eigenvectors of the time evolution operator. In this sense it is shown that when the relaxation modes are spatially delocalized, both...

Random walks on fractals and stretched exponential relaxation.

Stretched exponential relaxation [exp-(t/tau)(beta(K))] is observed in a large variety of systems but has not been explained so far. Studying random walks on percolation clusters in curved spaces whose dimensions range from 2 to 7, we show that the relaxation is accurately a stretched exponential and is directly connected to the fractal nature of these clusters. Thus we find that in each dimens...

Relationship between dynamical heterogeneities and stretched exponential relaxation.

We identify 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...

Stretched exponential relaxation and ac universality in disordered dielectrics