Intermittent relaxation in hierarchical energy landscapes.

We numerically simulate a thermalization process in an energy landscape with hierarchically organized metastable states. The initial configuration is chosen to have a large energy excess relative to the thermal equilibrium value at the running temperature. We show that the initial energy surplus is dissipated in a series of intermittent bursts, or quakes, whose rate decreases as the inverse of the age of the system. In addition, one observes energy fluctuations with a zero-centered Gaussian distribution. These pertain to the pseudoequilibrium dynamics within a single metastable state and do not contribute to the energy dissipation. The derivative of the thermal energy with respect to the logarithm of time is asymptotically constant and comprises a temperature-independent part and a part with an Arrhenius temperature dependence. The findings closely mirror recent numerical simulation results obtained for microscopic glassy models. For these models, record-sized energy fluctuations have been claimed to trigger intermittent events during low-temperature thermalization. In the present model record-sized fluctuations are by construction needed to trigger changes from one metastable state to another. This property thus suffices to explain the statistical property of intermittent energy flow in complex metastable systems.

Nonequilibrium dynamics in amorphous Si3B3N7.

We present extensive numerical investigations of the structural relaxation dynamics of a realistic model of the amorphous high-temperature ceramic a-Si3B3N7, probing the mean-square displacement of the atoms, the bond survival probability, the average energy, the specific heat, and the two-point energy average. Combining the information from these different sources, we identify a transition temperature Tc approximately 2000 K below which the system is no longer ergodic and physical quantities observed over a time t(obs) show a systematic parametric dependence on the waiting time t(w), or age, elapsed after the quench. The aging dynamics "stiffens" as the system becomes older, which is similar to the behavior of highly idealized models such as Ising spin glasses and Lennard-Jones glasses.

Aging and self-organized criticality in driven dissipative systems.

We study the noisy dynamics of a close relative to the original sandpile model. Depending on the type of noise and the time scale of observation, we find stationary fluctuations (similar to self-organized criticality) or an aging dynamics with punctuated equilibria, a decreasing rate of events and reset properties qualitatively similar to those of glassy systems, evolution models, and vibrated granular media.