Dimensional Hausdorff properties of singular continuous spectra

被引：45

作者：

Jitomirskaya, SY ^{[1
]}

Last, Y ^{[1
]}

机构：

[1] CALTECH,DIV PHYS MATH & ASTRON,PASADENA,CA 91125

来源：

PHYSICAL REVIEW LETTERS | 1996年 / 76卷 / 11期

关键词：

D O I：

10.1103/PhysRevLett.76.1765

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We present an extension of the Gilbert-Pearson theory of subordinacy, which relates dimensional Hausdorff spectral properties of one-dimensional Schrodinger operators to the behavior of solutions of the corresponding Schrodinger equation. We use this theory to analyze these properties for several examples having the singular-continuous spectrum, including sparse barrier potentials, the almost Mathieu operator and the Fibonacci Hamiltonian.

引用

收藏

页码：1765 / 1769

页数：5

相关论文

共 38 条

[1]

Aubry S., 1980, Annals of the Israel Physical Society, V3, P133

[2] ON THE MEASURE OF THE SPECTRUM FOR THE ALMOST MATHIEU OPERATOR [J].

AVRON, J ;

VONMOUCHE, PHM ;

SIMON, B .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1990, 132 (01) :103-118

[3] SINGULAR CONTINUOUS-SPECTRUM FOR A CLASS OF ALMOST PERIODIC JACOBI MATRICES [J].

AVRON, J ;

SIMON, B .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1982, 6 (01) :81-85

[4] SPECTRAL PROPERTIES OF ONE DIMENSIONAL QUASI-CRYSTALS [J].

BELLISSARD, J ;

IOCHUM, B ;

SCOPPOLA, E ;

TESTARD, D .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1989, 125 (03) :527-543

[5]

Carmona R., 1990, SPECTRAL THEORY RAND, DOI 10.1007/978-1-4939-0512-6_4

[6] OPERATORS WITH SINGULAR CONTINUOUS-SPECTRUM .2. RANK-ONE OPERATORS [J].

DELRIO, R ;

MAKAROV, N ;

SIMON, B .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1994, 165 (01) :59-67

[7] WHAT IS LOCALIZATION [J].

DELRIO, R ;

JITOMIRSKAYA, S ;

LAST, Y ;

SIMON, B .

PHYSICAL REVIEW LETTERS, 1995, 75 (01) :117-119

[8]

DELRIO R, IN PRESS OPERATORS S, V4

[9] ABSENCE OF LOCALIZATION IN THE ALMOST MATHIEU EQUATION [J].

DELYON, F .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1987, 20 (01) :L21-L23

[10] NEW CLASS OF LEVEL STATISTICS IN QUANTUM-SYSTEMS WITH UNBOUNDED DIFFUSION [J].

GEISEL, T ;

KETZMERICK, R ;

PETSCHEL, G .

PHYSICAL REVIEW LETTERS, 1991, 66 (13) :1651-1654

← 1 2 3 4 →