How dominant is the most efficient pathway through the potential energy landscape of a slowly diffusing disordered...

Area of Science:

• Physics
• Computational Science
• Statistical Mechanics

Background:

• Many-body systems exhibit slow diffusion, often attributed to complex potential energy landscapes.
• The geodesic path hypothesis suggests optimal pathways below a certain energy dictate diffusion efficiency.
• Understanding diffusion mechanisms is crucial in fields ranging from materials science to statistical physics.

Purpose of the Study:

• To test the geodesic path hypothesis for diffusion in low-dimensional percolation models.
• To investigate how path tortuosity and sparsity relate to vanishing diffusion constants.
• To compare the geodesic path formalism with traditional energy landscape models.

Main Methods:

• Application of geodesic path-finding approaches to 2D overlapping Lorentz model.
• Analysis of diffusion in square and simple-cubic bond-dilute lattices.
• Numerical simulations to evaluate model predictions against percolation phenomena.

Main Results:

• The geodesic path formalism did not fully describe diffusion in the weakly disordered (fast diffusion) limit for either model.
• However, the formalism successfully predicted the existence of percolation transitions.
• The models qualitatively supported the geodesic perspective, showing increased pathway tortuosity and sparsity as diffusion slowed.

Conclusions:

• The geodesic path perspective offers a valuable qualitative understanding of slow diffusion, especially near critical transitions.
• While not perfectly accurate in all regimes, the model highlights the importance of pathway geometry in diffusion processes.
• Further refinement of geodesic path-finding may enhance its predictive power for complex diffusion systems.