Pattern formations and relaxation dynamics in non-equilibrium systems

We present an investigation of two non-equilibrium systems: spatial many-species predator-prey games and systems of interacting magnetic skyrmions.

We numerically study two predator-prey systems characterized by nested pattern formations. We first consider a six species game in which spiral patterns spontaneously form within coarsening domains. Through a systematic investigation of relevant correlation functions, the interface width, and other quantities, we show that the non-trivial in-domain dynamics affect the coarsening process and the interfacial properties. The exponents which govern domain growth, aging, and interface fluctuations differ from those expected from curvature driven coarsening. The response to perturbations of the reaction rates is also studied. Furthermore, we introduce a nine species model characterized by nested spiral pattern formations. Quantitative evidence of the existence of two length and time scales associated to the spiral levels is presented in the form of correlation lengths and a temporal Fourier analysis of the species densities. A generalized interaction scheme is proposed for dynamically generated hierarchies.

Magnetic skyrmions are particle-like spin configurations found in certain chiral magnets. We study the effect of the Magnus force on the relaxation dynamics through Langevin molecular dynamics simulations. The Magnus force enhances the disorder of the system at high noise strengths while we observe a dynamic regime with slow decaying correlations at low noise strengths. The different regimes are characterized by changes in the aging exponent. In general, the Magnus force accelerates the approach to the steady state. In the presence of quenched disorder, we find that the relaxation dynamics are more robust in systems with a strong Magnus force. We also examine periodically driven skyrmion systems and show that a transition from reversible to irreversible flow exists in the presence of attractive defects. The Magnus force enhances the irreversible regime in this case.

The work on predator-prey systems was supported by the U.S. National Science Foundation through Grant No. DMR-1606814 whereas the work on skyrmions was supported by the US Department of Energy, Office of Basic Energy Sciences (DOE-BES), under Grant No. DE-FG02-09ER46613.