Research Paper#Statistical Physics, Diffusion, Energy Landscapes🔬 ResearchAnalyzed: Jan 3, 2026 20:17
Spatial Correlations Restore Mean-Field Diffusion in Rugged Landscapes
Analysis
This paper investigates the breakdown of Zwanzig's mean-field theory for diffusion in rugged energy landscapes and how spatial correlations can restore its validity. It addresses a known issue where uncorrelated disorder leads to deviations from the theory due to the influence of multi-site traps. The study's significance lies in clarifying the role of spatial correlations in reshaping the energy landscape and recovering the expected diffusion behavior. The paper's contribution is a unified theoretical framework and numerical examples that demonstrate the impact of spatial correlations on diffusion.
Key Takeaways
- •Zwanzig's mean-field theory can fail in rugged energy landscapes with uncorrelated disorder.
- •Multi-site traps are a key reason for the failure of the mean-field theory.
- •Gaussian spatial correlations can suppress these traps and restore the validity of the mean-field theory.
- •The paper provides a theoretical framework and numerical examples to support these findings.
Reference
“Gaussian spatial correlations reshape roughness increments, eliminate asymmetric multi-site traps, and thereby recover mean-field diffusion.”