Nonergodic subdiffusion from Brownian motion in an inhomogeneous medium.

Area of Science:

• Physics
• Physical Chemistry
• Statistical Mechanics

Background:

• Nonergodicity in single-particle tracking experiments is often attributed to transient trapping.
• Existing models may not fully capture the complexity of diffusion in disordered environments.

Purpose of the Study:

• To introduce and analyze models of Brownian motion in media with spatially varying diffusion coefficients and region sizes.
• To investigate the origins of nonergodicity and subdiffusion in such heterogeneous systems.

Main Methods:

• Development of theoretical models for a diffusing particle in a medium with random region sizes and diffusivities.
• Mathematical analysis of the mean squared displacement under annealed and quenched disorder assumptions.
• Formulation of the model as a continuous-time and continuous-space random walk, analogous to Lévy walks.

Main Results:

• The proposed models demonstrate that nonergodicity and subdiffusion arise naturally from spatial disorder, even without particle trapping.
• Analytical solutions show subdiffusive behavior in the mean squared displacement for both annealed and quenched disorder.
• The model's continuous nature connects it to established anomalous diffusion frameworks like Lévy walks.

Conclusions:

• Spatial disorder, characterized by random region sizes and diffusivities, is a sufficient explanation for observed nonergodicity and subdiffusion in particle tracking.
• The developed models provide a robust alternative to transient trapping explanations for anomalous diffusion.
• This work offers a new perspective on modeling complex diffusion phenomena in heterogeneous materials.