不公度相及公度-不公度相变:一维情形

INCOMMENSURATE PHASES AND COMMENSURATE INCOMMENSURATE TRANSITIONS: ONE DIMENSIONAL CASE

本文通过ＦｒｅｎｋｅｌＫｏｎｔｏｒｏｖａ（ＦＫ）模型评述了凝聚态物理中的一个重要课题：不公度相和公度不公度（ＣＩ）相变。论述主要集中在一维情形，对不公度相和ＣＩ相变的概念、物理图象、产生机制、研究背景、研究目标和意义进行了必要的介绍；概述了早期、近期和现代研究过程中一些典型的基本理论和方法；对标准ＦＫ模型及原子间势为凸函数的ＦＫ模型、经典非凸ＦＫ模型、ＦＫ模型的量子效应、一维双原子链ＦＫ模型、ＦＫ模型向二维和三维的推广、ＣＩ相变的有限温度效应等专题的研究进展作了概述，并指出了一些有待进一步探讨的课题。

An important project, incommensurate phases and commensurate incommensurate (CI) transitions, in condensed matter physics is reviewed through the Frenkel Kontorova(FK) model. The reviews mainly focus on the one dimensional case. We present the concepts, physical pictures, mechanism, backgroud, objects and significance of the incommensurate phases and CI transitions. Some basic theories and methods in the studies are given. We briefly reviewed the advances of some special topics which include the standard FK model and the generalized ones with convex interatomic interactions, the classical nonconvex FK model, the quantum effects of the FK model, the FK model with one dimensional diatomic chain, the generalization of the FK modle to two dimenisonal and three dimensional cases, the finite temperature effects of CI transitions. We also present some topics which need more investigation.