Topologically Protected Metastable States in Classical Dynamics

Han-Qing Shi, Tian-Chi Ma, Hai-Qing Zhang

Published 2023-11-13Version 1

We propose that the domain walls formed in a classical Ginzburg-Landau model can exhibit topologically stable but thermodynamically metastable states. This proposal relies on Allen-Cahn's assertion that the velocity of domain wall at some point is proportional to the mean curvature at that point. From this assertion we speculate that domain wall resembles a rubber band that can winds the background geometry in a nontrivial way and can exist permanently. We numerically verify our proposal in two and three spatial dimensions by using periodic boundary conditions as well as Neumann boundary conditions. We find that there are always possibilities to form topologically stable domain walls in the final equilibrium states. However, from the aspects of thermodynamics these topologically nontrivial domain walls have higher free energies and are thermodynamically metastable. These metastable states that are protected by topology could potentially serve as storage media in the computer and information technology industry.