RUI: Roughened Manifolds in Ill-Condensed Matter

这是本科生研究所授予的一项研究，目的是对各种表面的静态和动态标度特性进行理论研究，这些表面由于热波动而表现出熵粗糙，但在存在淬火无序(以随机分布的钉扎杂质的形式)时可能会导致漂移，漂移会增强许多倍。有许多具有重大实践意义的基本理论问题，这些问题源于热和无序诱导的粗糙化之间的微妙相互作用。这自然源于这样一个事实，即大多数实验系统在某种程度上都是病态凝聚物质的形式；极小的随机性不仅对临界性质，而且对相图的整个整体结构都有潜在的严重影响。在将要讨论的各种流形中，包括陶瓷超导体中的单个涡旋线，随机介质中的定向聚合物，以及受杂质打击的磁体中的磁畴壁。通过Burgers方程的映射，我们可以将定向聚合物问题与弹道沉积和伊甸团簇等随机生长模型联系起来。还讨论了由于Abrikosov磁通线晶格的淬火无序和杂质控制的扭曲引起的界面离域效应。巴纳德学院将进行分析和计算研究，研究无序对表面的一般性质的影响及其在聚合物、超导体和磁体等特定物理系统中的表现。这项工作将利用本科生。

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.