Abstract

Physics Nobel Prize winner P.W. Anderson famously wrote in 1995: “The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of the glass and the glass transition”. Despite much effort in the intervening years, the problem is still unsolved. We contribute a novel mathematical approach to this problem. The main new ingredient is finite dimension, a recently introduced “fractal” dimension defined only for finite sets. Our methods sharply distinguish the glass transition temperature and give hints as to the structural changes that occur in the transition.

Graphic Abstract

中文翻译：

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有限维揭示了玻璃化转变的结构特征

摘要

物理学诺贝尔奖获得者 PW Anderson 在 1995 年写下著名的文章：“固态理论中最深刻、最有趣的未解决问题可能是关于玻璃的性质和玻璃化转变的理论”。尽管在此期间付出了很多努力，但问题仍未得到解决。我们为这个问题贡献了一种新颖的数学方法。主要的新成分是有限维，这是最近引入的仅针对有限集定义的“分形”维。我们的方法清晰地区分了玻璃化转变温度，并提示了转变过程中发生的结构变化。

图形摘要