一类非公度体系的量子动力学性质

QUANTUM DYNAMICS IN A INCOMMENSURATE SYSTEM

研究了格点势能Ｖｎ＝λｔａｎｈ［Ａｃｏｓ（２πσｎ）］／ｔａｎｈＡ，（σ＝（５－１）／２）的一类非公度体系的量子动力学性质，着重分析了自关联函数Ｃ（ｔ）在不同哈密顿量参数区域的长时行为，并讨论了自关联函数Ｃ（ｔ）与能谱关联维数Ｄ２的关系．结果表明：当ｔ→∞和ｌ→０时，Ｃ（ｔ）～ｔ－δ，Ｒ（ｌ）～ｌＤ２，且Ｄ２＝δ．随着λ的增大，存在两个临界参数λＣ１和λＣ２，当０＜λ＜λＣ１Ｃ（ｔ）～ｔ－１，当λＣ１＜λ＜λＣ２时，Ｃ（ｔ）～ｔ－δ，０＜δ＜１；而当λ＞λＣ２时，Ｃ（ｔ）～ｔ０，电子被局域在初始位置．临界点λＣ１和λＣ２的大小依赖于参数Ａ的大小．

We study the quantum dynamics in an incommensurate system with potentials Vn=λtanh[Acos (2πσn)]/tanhA,where σ=(5-1)/2.Particular attention is paid to the analysis of long-time behavior of autocorrelation function C(t) and the relationship between C(t) and spectrum probility R(l). With the increase of λ,we find two critical values (λC1and λC2),which are related to parameter A. When 0<λ<λC1,numerical calculations show that C(t)～t-1,which corresponds to the case of periodic systems. For the case of λC1<λ<λC2,C(t)～t-δwith 0<δ<1. When λ>λC2,C(t)～t0,and the electron is localized.