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
[31]   ABSENCE OF LOCALIZATION IN CERTAIN STATICALLY DISORDERED LATTICES IN ANY SPATIAL DIMENSION [J].
DUNLAP, DH ;
KUNDU, K ;
PHILLIPS, P .
PHYSICAL REVIEW B, 1989, 40 (16) :10999-11006
[32]   THE KRONIG-PENNEY MODEL ON A GENERALIZED FIBONACCI LATTICE [J].
GHOSH, PK .
PHYSICS LETTERS A, 1991, 161 (02) :153-157
[33]   MULTIFRACTAL ANALYSIS IN RECIPROCAL SPACE AND THE NATURE OF THE FOURIER-TRANSFORM OF SELF-SIMILAR STRUCTURES [J].
GODRECHE, C ;
LUCK, JM .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1990, 23 (16) :3769-3797
[34]   NONPERIODIC ISING QUANTUM CHAINS AND CONFORMAL-INVARIANCE [J].
GRIMM, U ;
BAAKE, M .
JOURNAL OF STATISTICAL PHYSICS, 1994, 74 (5-6) :1233-1245
[35]  
HOF A, 1994, SINGULAR CONTINUOUS
[36]  
HOF A, 1992, QUASI CRYSTALS PERIO
[37]   3 CLASSES OF ONE-DIMENSIONAL, 2-TILE PENROSE TILINGS AND THE FIBONACCI KRONIG-PENNEY MODEL AS A GENERIC CASE [J].
HOLZER, M .
PHYSICAL REVIEW B, 1988, 38 (03) :1709-1720
[38]   SINGULAR CONTINUOUS ELECTRON SPECTRUM FOR A CLASS OF CIRCLE SEQUENCES [J].
HORNQUIST, M ;
JOHANSSON, M .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1995, 28 (02) :479-495
[39]   ELECTRON TRANSMISSION IN A ONE-DIMENSIONAL QUASI-CRYSTAL [J].
HU, P ;
TING, CS .
PHYSICAL REVIEW B, 1986, 34 (12) :8331-8334
[40]   POWER LAW GROWTH FOR THE RESISTANCE IN THE FIBONACCI MODEL [J].
IOCHUM, B ;
TESTARD, D .
JOURNAL OF STATISTICAL PHYSICS, 1991, 65 (3-4) :715-723