关于一维三元准周期模型的讨论

DISCUSSION ON ONE-DOMENSIONAL TERNARY QUASIPERIODIC MODELS

研究了替代关系为Ａ→ＡＢ，Ｂ→Ｃ，Ｃ→Ａ序列上的一维三元类Ｆｉｂｏｎａｃｃｉ模型的结构、能谱和波函数的性质，发现这个模型以无序性为主要特征，准周期性表现的并不明显，不应作为理论研究中的准周期模型．我们给出一个替代关系为Ａ→ＡＢＣ，Ｂ→Ａ，Ｃ→Ｂ序列上的三元广义Ｆｉｂｏｎａｃｉ模型，呈现出明显的准周期性，可作为一个三元准周期模型进一步讨论．

The Fourier transformation of the sequence,the energy spectrum and second moments of the wavefunctions have been studied for a one dimensional ternary model generated by the substitution A→AB,B→C,C→A ,commonly called ternary Fibonacci class model.It is found that this model behaves disordered features,it should not be regarded as a quasiperiodic model in theoretical studies.A ternary general Fibonacci model generated by the substitution A→ABC,B→A,C→B was proposed in this paper,which behaves abvious quasiperiodic features.This model can be convinced a quasiperiodic model for further discussion.