Geometric Phases in Particle Diffusion with Non-Hermitian Hamiltonian Structures

Geometric phases in particle diffusion systems offer a different understanding beyond traditional Brownian motion and Fick’s laws. Here we introduce a unique structure composed of two rings moving in opposite directions and a stationary intermediate layer, which plays multifunctional roles in controlling particle diffusion. Numerical simulations using COMSOL Multiphysics validate the theoretical framework and provide deeper insights into the behavior of geometric phase. We also describe a bilayer particle-diffusion cloak, illustrating its simple design and adaptable control mechanisms. This system has potential applications in industries like healthcare and environmental management, thus expanding the understanding of the geometric phase and offering insights for the design of particle-diffusion metamaterials.