论文标题
没有远距离空间秩序的物质不均阶段的理论方法
A measure theoretical approach to non-uniform phases of matter with no long-range spatial order
论文作者
论文摘要
在本文中，提出了一种数学方法的开发，以探索一阶相变的数学模型中没有长距离顺序的空间不均匀阶段。我们使用有关测量现象浓度的基本结果来重新构建部分微分方程以进行概率度量，这将分析解决方案的概念扩展到了随机场。方程式的随机解是一种非单明的概率度量，根据该度量，随机变量几乎肯定是方程式的解决方案。一般概念应用于连续理论，其中对称性破裂的概念扩展到概率度量。该概念是对一阶相变的非本地连续性平均场理论的可行和预测。结果表明，在概率度量的水平上，对称性破裂必须存在于能量的随机固定点中。这与观察到无定形固体结构保持局部排序的观察是一致的。
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the concentration of measure phenomenon to re-formulate partial differential equations for probability measures, which extends the concept of analytical solutions to random fields. A stochastic solution of an equation is such a non-singular probability measure, according to which the random variable is almost surely a solution to the equation. The general concept is applied for continuum theories, where the concept of symmetry breaking is extended to probability measures. The concept is practicable and predictive for non-local continuum mean-field theories of first order phase transitions. The results suggest that symmetry breaking must be present in stochastic stationary points of the energy on the level of the probability measure. This is in agreement with the observation that amorphous solid structures preserve local ordering.
