在存在空间相关性的情况下，粗糙能量景观中的扩散：一个令人惊讶的通往Zwanzig平均场预测的路线
Diffusion in Rugged Energy Landscapes in the Presence of Spatial Correlations : A Surprising Route to Zwanzig's Mean-Field Prediction
AI总结：
本文提出统一理论框架，阐明空间相关性如何重塑粗糙度并恢复平均场扩散，同时揭示不相关无序对Zwanzig理论的破坏作用。
摘要：
在化学物理、生物分子动力学、聚合物运输和许多无序系统中，粗糙自由能景观中的扩散是核心问题。Zwanzig著名的经典平均场理论预测，粗糙度通过仅由无序方差决定的指数因子减少扩散系数。然而，Banerjee、Seki和Bagchi（BSB）的数值研究显示，对于不相关的高斯分布位点能量，这一结果在长时传输中失效，因为罕见但深的三站点陷阱主导了传输。BSB引入了高斯空间相关性——最初在天体物理中开发以建模湍流密度波动——并证明即使适度的相关性也能抑制这些病态陷阱并恢复Zwanzig的指数缩放。本文提出一个统一的理论框架，阐明（i）为什么Zwanzig的局部平均可能被视为高斯累积展开，可能失效。特别是，如何其有效性被不相关无序破坏；（ii）如何高斯空间相关性重塑粗糙度增量，消除不对称多站点陷阱，并因此恢复平均场扩散；（iii）推导显示高斯空间相关性如何修改粗糙度增量、陷阱统计学以及最终的扩散常数。我们还提供了具体的数值三元组示例，说明空间相关性如何大幅减少逃逸时间。
英文摘要：
Diffusion in rugged free-energy landscapes is central to diverse problems in chemical physics, biomolecular dynamics, polymer transport and numerous disordered systems. Zwanzig's well-known classic mean-field theory predicts that roughness reduces the diffusion coefficient by an exponential factor determined solely by the variance of the disorder. However, the numerical studies of Banerjee, Seki, and Bagchi (BSB) showed that this result fails for uncorrelated Gaussian-distributed site energies because rare but deep three-site traps dominate long-time transport. BSB introduced Gaussian \emph{spatial} correlations - originally developed in astrophysics to model turbulent density fluctuations - and demonstrated that even modest correlations suppress these pathological traps and restore Zwanzig's exponential scaling. Here we present here a unified theoretical framework clarifying (i) why Zwanzig's local averaging, may be viewed as a Gaussian cumulant expansion, could breakdown. In particular, how its validity is destroyed by uncorrelated disorder, and (ii) how Gaussian spatial correlations reshape roughness increments, eliminate asymmetric multi-site traps, and thereby recover mean-field diffusion, and (iii) a derivation showing exactly how Gaussian spatial correlations modify roughness increments, trap statistics, and ultimately the diffusion constant. We also provide explicit numerical triplet examples illustrating the dramatic reduction of escape times produced by spatial correlations.
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