RUI: Transitions in Quasiperiodic and Hierarchical Systems

这项研究的目的是研究各种具有竞争长度的准周期、多层次和复杂系统，重点是研究这些系统中发生的各种转变。非线性动力学的概念和工具将被用来理解和描述这些转变背后的奇异行为。主要的研究领域是：了解和表征自旋系统的长程有序，如准周期Fibonacci链、Thue-Morse链、具有超度量拓扑的层次化自旋系统；具有分形相边界的自旋、电子和声子系统的级联跃迁以及离散映射中的准周期到混沌的跃迁。

The proposed research is to study a variety of quasiperiodic, hierarchical and complex systems with competing lengths, with main emphasis being the study of various transitions which occur in these systems. The concepts and tools of nonlinear dynamics will be used in understanding and characterizing the exotic behavior underlying these transitions. The major areas of investigation are: understanding and characterizing the long range order in spin systems such as quasiperiodic Fibonacci chains, Thue-Morse chains, hierarchical spin systems with ultrametric topology; spin, electron and phonon systems exhibiting cascades of transitions with fractal phase boundaries and quasiperiodic transitions to chaos in discrete maps.