REMARKS ON THE SPECTRAL PROPERTIES OF TIGHT-BINDING AND KRONIG-PENNEY MODELS WITH SUBSTITUTION SEQUENCES

被引:73
作者
BOVIER, A
GHEZ, JM
机构
[1] CNRS MARSEILLE LUMINY, CTR PHYS THEOR, F-13288 MARSEILLE 9, FRANCE
[2] UNIV TOULON & VAR, DEPT MATH, PHYMAT, F-83957 LA GARDE, FRANCE
来源
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 1995年 / 28卷 / 08期
关键词
D O I
10.1088/0305-4470/28/8/022
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We comment on some recent investigations on the electronic properties of models associated with the Thue-Morse chain, point out that their conclusions contradict rigorously proven theorems, and indicate some of the sources of these misinterpretations. We briefly review and explain the current status of mathematical results in this field and discuss some conjectures and open problems.
引用
收藏
页码:2313 / 2324
页数:12
相关论文
共 77 条
[1]  
ALLOUCHE JP, 1986, CR ACAD SCI II, V302, P1135
[2]   MINIMUM-DIMENSION TRACE MAPS FOR SUBSTITUTION SEQUENCES [J].
AVISHAI, Y ;
BEREND, D ;
GLAUBMAN, D .
PHYSICAL REVIEW LETTERS, 1994, 72 (12) :1842-1845
[3]   TRANSMISSION THROUGH A FIBONACCI CHAIN [J].
AVISHAI, Y ;
BEREND, D .
PHYSICAL REVIEW B, 1991, 43 (09) :6873-6879
[4]   TRANSMISSION THROUGH A THUE-MORSE CHAIN [J].
AVISHAI, Y ;
BEREND, D .
PHYSICAL REVIEW B, 1992, 45 (06) :2717-2724
[5]   HIGH-RESOLUTION X-RAY-DIFFRACTION SPECTRA OF THUE-MORSE GAAS-ALAS HETEROSTRUCTURES - TOWARDS A NOVEL DESCRIPTION OF DISORDER [J].
AXEL, F ;
TERAUCHI, H .
PHYSICAL REVIEW LETTERS, 1991, 66 (17) :2223-2226
[6]   SPECTRUM AND EXTENDED STATES IN A HARMONIC CHAIN WITH CONTROLLED DISORDER - EFFECTS OF THE THUE-MORSE SYMMETRY [J].
AXEL, F ;
PEYRIERE, J .
JOURNAL OF STATISTICAL PHYSICS, 1989, 57 (5-6) :1013-1047
[7]   VIBRATIONAL-MODES IN A ONE-DIMENSIONAL QUASI-ALLOY - THE MORSE CASE [J].
AXEL, F ;
ALLOUCHE, JP ;
KLEMAN, M ;
MENDESFRANCE, M ;
PEYRIERE, J .
JOURNAL DE PHYSIQUE, 1986, 47 (C-3) :181-186
[8]   PERIODIC CLUSTERING IN THE SPECTRUM OF QUASI-PERIODIC KRONIG-PENNEY MODELS [J].
BAAKE, M ;
JOSEPH, D ;
KRAMER, P .
PHYSICS LETTERS A, 1992, 168 (03) :199-208
[9]   TRACE MAPS, INVARIANTS, AND SOME OF THEIR APPLICATIONS [J].
BAAKE, M ;
GRIMM, U ;
JOSEPH, D .
INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 1993, 7 (6-7) :1527-1550
[10]  
BAAKE M, 1995, IN PRESS J STAT PHYS