RUI: Roughened Manifolds in Ill-Condensed Matter

这是一项本科院校的研究拨款，用于开展关于各种表面的静态和动态缩放特性的理论研究，这些表面由于热波动而表现出熵粗化，但在淬火无序（以随机分布的钉住杂质的形式）的存在下，可能导致漫游增强许多倍。热粗化和无序粗化之间微妙的相互作用产生了许多具有重要实际意义的基本理论问题。这是由于大多数实验系统在某种程度上都是非凝聚态物质的形式；最小的随机性不仅对关键性质有潜在的剧烈影响，而且对相图的整个整体结构也有潜在的剧烈影响。要讨论的流形包括陶瓷超导体中的个别涡旋线、随机介质中的定向聚合物和受杂质影响的磁体中的畴壁。通过Burgers方程的映射使我们能够将定向聚合物问题与随机生长模型（如弹道沉积和Eden簇）联系起来。还考虑了由于淬火无序和杂质控制的Abrikosov通量线晶格畸变引起的界面离域。巴纳德学院将进行分析和计算研究，研究无序对表面一般性质的影响，以及它们在特定物理系统（如聚合物、超导体和磁铁）中的表现。这项工作将利用大学生。

This is a Research at Undergraduate Institution grant to conduct theoretical research concerning the static and dynamic scaling properties of a variety of surfaces which exhibit entropic roughening due to thermal fluctuations, but in the presence of quenched disorder (in the form of randomly distributed pinning impurities) can lead to wandering that is enhanced many-fold. There are a number of fundamental theoretical issues of great practical importance which arise from the delicate interplay between thermal and disorder-induced roughening. This follows naturally from the fact that most experimental systems are to some degree forms of ill-condensed matter; the smallest modicum of randomness having potentially drastic effects upon not merely the critical properties, but the entire global structure of the phase diagram. Among the various manifolds to be discussed are individual vortex lines in ceramic superconductors, directed polymers in random media, and domain walls in impurity-stricken magnets. A mapping via Burgers equation permits us to connect the directed polymer problem to stochastic growth models such as ballistic deposition and Eden clusters. Also considered are interfacial delocalization due to quenched disorder and impurity controlled distortions of Abrikosov flux line lattices. %%% Analytical and computational research will be conducted at Barnard College on the effects of disorder on the general properties of surfaces and their manifestations in particular physical systems such as polymers, superconductors and magnets. The work will utilize undergraduates.