When spatial disorder matters: from ultra-slow dynamics to pole-to-pole oscillation

Valentin Anfray^1*, Hong-Yan Shih¹

¹Institute of Physics, Academia Sinica, Taipei, Taiwan

* Presenter:Valentin Anfray, email:valentin.anfray@gmail.com

We investigate how spatial heterogeneity alters the critical properties of a reaction-diffusion system compared to its homogeneous counterpart. Our study uses a minimal two-species model, a building block for understanding systems with positive feedback, such as epidemics or cellular processes.

Combining Kinetic Monte-Carlo simulations with analytical results, we demonstrate that disorder dramatically alters the system's critical properties. This leads to the emergence of exotic fixed points with dynamics slower than conventional power laws, surrounded by Griffiths phases that exhibit power-law relaxation.

Such disorder-induced critical slowing down has significant biological implications. We illustrate this principle by showing that robust pole-to-pole oscillations in a cell could emerge from the simple interplay between a positive feedback loop and spatial disorder, which can represent various physical features, such as the cell's non-uniform geometry.

Keywords: non-equilibrium statistical physics, phase transition, spatial quenched disorder, stochastic oscillations