近日，美国杜克大学Patrick Charbonneau团队研究了随机洛伦兹气体中干扰算法的几何特性。该研究于2025年11月5日发表在《美国科学院院刊》杂志上。

确定性优化算法将复杂能量景观明确划分为本征结构及其对应的吸引域。这些吸引域能否仅通过几何原理定义？这对理解作为无序物质关键模型的硬球阻塞现象至关重要。

研究组通过提出一类几何类梯度下降算法来研究该问题，并以此研究硬球普适性类别中的随机洛伦兹气体系统。研究发现，所得本征结构的统计特性严格继承自泊松-沃罗诺伊镶嵌的统计规律。进一步发现能量景观的粗糙度导致本征结构呈现层级化组织，不同算法会以不同方式探索这些结构。

特别值得注意的是，激进型与保守型算法会倾向于选择密度显著不同的本征结构。然而，最终获得的本征结构均稳健地呈现出统一的力分布规律，由此证实了阻塞普适性类别具有几何本质。在研究过程中，研究组还揭示了动力学加德纳相变的物理起源。

附：英文原文

Title: The geometry of jamming algorithms in the random Lorentz gas

Author: Folena, Giampaolo, Charbonneau, Patrick, Morse, Peter K., Rojas, Rafael Díaz Hernández, Ricci-Tersenghi, Federico

Issue&Volume: 2025-11-5

Abstract: Deterministic optimization algorithms unequivocally partition a complex energy landscape into inherent structures (ISs) and their respective basins of attraction. Can these basins be defined solely through geometric principles This question is paramount to understanding hard sphere jamming, a key model of disordered matter. We here address the issue by proposing a geometric class of gradient descent–like algorithms, which we use to study a system in the hard-sphere universality class, the random Lorentz gas. The statistics of the resulting ISs is found to be strictly inherited from those of Poisson–Voronoi tessellations. The landscape roughness is further found to give rise to a hierarchical organization of ISs, which various algorithms explore differently. In particular, greedy and reluctant schemes tend to favor ISs of markedly different densities. The resulting ISs nevertheless robustly exhibit a universal force distribution, thus confirming the geometric nature of the jamming universality class. Along the way, the physical origin of a dynamical Gardner transition is identified.

DOI: 10.1073/pnas.2422096122

Source: https://www.pnas.org/doi/abs/10.1073/pnas.2422096122