Presidential Young Investigator Award

研究计划将包括：(A)准晶生长和结构。在真正的准晶中观察到的无序是物质的这一阶段所固有的，还是仅仅是非最佳生长条件的结果，仍然存在很大的争议。一种特殊的非平衡生长模型似乎在定性和定量上重现了在衍射实验中观察到的无序。我们将设计一个更明确的比较，因为这个模型产生的结构非常明确地被描述为具有内在无序，类似于玻璃。通过使用比以前更定量的电子显微镜，可以在这一方向上取得进展。(B)低温物理。除了Nagaoka和Thouless在60年代的工作外，令人惊讶的是，人们对自旋1/2粒子(电子，3He)晶格中空穴(空位)的运动知之甚少(即使是定性的)。例如：(1)当引入有限密度的空穴时，二分晶格中的单个空穴诱导的铁磁性是稳定的吗？(2)三角形(非二分)晶格中的单个空穴诱导的磁有序形式是什么？这些都是最简单、高度相关的费米子系统，它们不是微不足道的，完全缺乏直观的理解。通过使用试波函数和各种其他计算技术，这些和类似的问题将被调查。

The research plan will consist of: (a) Quasicrystal growth and structure. There is still a great deal of controversy whether the disorder observed in real quasicrystals is intrinsic to this phase of matter or just a consequence of non-optimal growth conditions. A particular non-equilibrium model of growth appears to reproduce both qualitatively and quantitatively the disorder observed in diffraction experiments. A more difinitive comparision will be devised since the structures generated by this model very definitely are characterized as having intrinsic disorder, similar to a glass. Progress in this direction may be made by using the electron microscope in a more quantitative capacity than previously. (b) Low temperature physics. Beyond the work of Nagaoka and Thouless in the 60`s, surprisingly little is understood (even qualitatively) about the motion of a hole (vacancy) in a lattice of spin 1/2 particles (electrons, 3He). Examples: (1) Is the ferromagnetism induced by a single hole in a bipartite lattice stable when a finite density of holes is introduced? (2) What form of magnetic ordering is induced by a single hole in a triangular (nonbipartite) lattice? These are among the simplest, highly correlated fermion systems which are nontrivial and for which an intuitive understanding is completely lacking. Through the use of trial wavefunctions and various other computational techniques, these and similar problems will be investigated.