Temporal statistics of thermal creep dynamic in 1+1 dimensional surface growth

This study examines the dynamics of elastic interfaces in disordered media, focusing on thermal creep avalanches and their statistical similarities to aftershock sequences. In non-thermal settings, interface motion under external force is governed by a "depinning transition," where movement begins only when the force exceeds a critical threshold. However, when external forces act slowly and internal relaxation cannot be ignored, a complex "creep avalanche" emerges, exhibiting rich dynamical behavior that depends on factors like temperature.

Recent studies indicate that avalanche behavior during relaxation exhibits statistical patterns similar to aftershocks, as described by the Omori-Utsu law in seismology. To investigate these similarities and identify the conditions for aftershock-like behavior, we use the Fluctuation Line Model to study the spatiotemporal dynamics of creep avalanches. This model is applicable to various depinning phenomena, such as magnetic domain-wall motion and crack propagation.

Our statistical analysis examines how loading speed influence the creep avalanche behavior, revealing insights into both the similarities and distinctions in the statistical behavior of different systems. This work broadens the understanding of surface growth with relaxation effects and provides a foundation for further exploration into the universal properties of complex dynamical systems.