RUI: Transitions in Quasiperiodic and Hierarchical Systems

本文拟研究具有竞争长度的各种准周期、分层和复杂系统，重点研究这些系统中发生的各种过渡。非线性动力学的概念和工具将用于理解和描述这些转变背后的奇异行为。主要研究领域是：理解和表征自旋系统中的长范围有序，如准周期斐波那契链、Thue-Morse链、具有超超拓扑结构的分层自旋系统；在离散映射中表现出具有分形相边界的级联跃迁和准周期跃迁到混沌的自旋、电子和声子系统。

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.