Theoretical Problems in Condensed Matter and Statistical Physics

9417047纳尔逊这项研究是在凝聚态理论的一系列主题，包括柱状液晶，高温超导体中的涡旋输运和钉扎以及二维自旋系统中的波动。 重点是缺陷，中间程度的秩序，几何和统计力学之间的相互作用。 柱状液晶通常由半柔性聚合物组成，提供了部分有序系统的迷人例子，其材料特性受线性空位和间隙缺陷的影响。 这种缺陷在点状粒子的集合体中是没有类似的。 当聚合物是手性的时，如在DNA或多肽聚（γ-谷氨酸苄酯）（PBG）中，会出现另外的挑战性问题。 半导体中磁通钉扎的工作是针对预测最佳的涡旋钉扎结构，如由重离子辐射引起的张开的柱状缺陷。 要完全理解由此产生的“张开的玻璃”和通量液相，需要在等效多体玻色子问题中扩展量子力学，以允许淬灭的随机虚矢势。 还计划对固定障碍物周围的涡旋近场和纠缠进行研究。 在柔性聚合膜中存在的平面相和连续对称性破缺引起了关于二维中密切相关的自旋系统的有趣问题。 调查将作出一个并矢自旋模型之间的海森伯类系统，其中真正的长程秩序是不可能的，和tetraxis膜，现在已经观察到实验表现出连续的破缺。 在某些液晶聚合物，高温超导体和磁性材料中出现的几何和统计力学之间的相互作用将被研究。 聚合物液晶相，例如由生物材料如DNA双螺旋和某些人工蛋白质制备的那些，可以受到手性效应的强烈影响，即，因为这些大分子缺乏镜像对称性。 人们希望研究空位和间隙缺陷，并了解如何手性可以导致这种聚合物自发编织。 这项工作可能最终导致合成更强的聚合物材料的策略。 新的高温超导体的许多应用需要有效地钉扎被称为涡旋的量子化磁场线。 在额外的工作中，将寻找在下面的晶体中的缺陷的最佳排列，这些缺陷将涡旋固定在适当的位置。 最后，研究了一类特殊的磁性材料的有序度与片状聚合物的起皱之间的关系。

9417047 Nelson This research is on a range of topics in condensed matter theory, including columnar liquid crystals, vortex transport and pinning in high-temperature superconductors and fluctuations in two- dimensional spin systems. The emphasis is on defects, intermediate degrees of order, and the interplay between geometry and statistical mechanics. Columnar liquid crystals, often composed of semiflexible polymers, provide fascinating examples of partially ordered systems, with material properties influenced by linear vacancy and interstitial defects. Such defects have no analogue in assemblies of point-like particles. Additional challenging problems arise when the polymers are chiral, as in DNA or the polypeptide poly (y-benzyl glutamate) (PBG). Work on flux pinning in semiconductors is directed at predicting optimal vortex pinning structures, such as splayed columnar defects induced by heavy ion radiation. A complete understanding of the resulting "splayed glass" and flux liquid phases requires an extension of quantum mechanics in the equivalent many-body boson problem to allow for a quenched random imaginary vector potential. Studies of vortex smectics and entanglement around fixed obstacles are also planned. The existence of the flat phase and a continuous broken symmetry in flexible polymerized membranes raises interesting questions about closely related spin systems in two dimensions. Investigations will be made on a dyadic spin model which interpolates between Heisenberg-like systems, for which genuine long-range order is impossible, and tehered membranes, which have now been observed experimentally to exhibit continuous symmetry-breaking. %%% The interplay between geometry and statistical mechanics which arises in certain liquid crystalline polymers, in high temperature superconductors, and in magnetic materials will be studied. Polymer liquid crystal phases, such as those prepared from biological materials, like DNA double helix and certain a rtificial proteins, can be strongly influenced by the effects of chirality, i.e., by the lack of mirror symmetry in these macromolecules. It is hoped to investigate vacancy and interstitial defects, and to understand how chirality can cause such polymers to braid up spontaneously. This work may eventually lead to strategies for synthesizing stronger polymeric materials. Many applications of the new high temperature superconductors require efficient pinning of quantized lines of magnetic field called vortices. In additional work, optimal arrangements of defects in the underlying crystal which pin the vortices in place will be searched. Finally, the relationship between oder in a special class of magnetic materials and the crumpling of sheet polymers will be studied.