Eigenfunction Entropy and Spectral Compressibility for Critical Random Matrix Ensembles

被引：63

作者：

Bogomolny, E. ^{[1
]}

Giraud, O. ^{[1
]}

机构：

[1] Univ Paris 11, CNRS, LPTMS, UMR 8626, F-91405 Orsay, France

来源：

PHYSICAL REVIEW LETTERS | 2011年 / 106卷 / 04期

关键词：

ANDERSON TRANSITION; LEVEL COMPRESSIBILITY; DIPOLE INTERACTION; VIBRATIONAL-MODES;

D O I：

10.1103/PhysRevLett.106.044101

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Based on numerical and perturbation series arguments we conjecture that for certain critical random matrix models the information dimension of eigenfunctions D(1) and the spectral compressibility chi are related by the simple equation chi + D(1)/d = 1, where d is system dimensionality.

引用

页数：4

共 21 条

[1] Random Matrix Ensembles Associated with Lax Matrices [J].

Bogomolny, E. ;

Giraud, O. ;

Schmit, C. .

PHYSICAL REVIEW LETTERS, 2009, 103 (05)

[2]

BOGOMOLNY E, IN PRESS

[3] Spectral rigidity and eigenfunction correlations at the Anderson transition [J].

Chalker, JT ;

Kravtsov, VE ;

Lerner, IV .

JETP LETTERS, 1996, 64 (05) :386-392

[4] PERCOLATION, QUANTUM TUNNELLING AND THE INTEGER HALL-EFFECT [J].

CHALKER, JT ;

CODDINGTON, PD .

JOURNAL OF PHYSICS C-SOLID STATE PHYSICS, 1988, 21 (14) :2665-2679

[5] Multifractality at the quantum Hall transition: Beyond the parabolic paradigm [J].

Evers, F. ;

Mildenberger, A. ;

Mirlin, A. D. .

PHYSICAL REVIEW LETTERS, 2008, 101 (11)

[6] Anderson transitions [J].

Evers, Ferdinand ;

Mirlin, Alexander D. .

REVIEWS OF MODERN PHYSICS, 2008, 80 (04) :1355-1417

[7] The Anderson localization transition and eigenfunction multifractality in an ensemble of ultrametric random matrices [J].

Fyodorov, Yan V. ;

Ossipov, Alexander ;

Rodriguez, Alberto .

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2009,

[8] Spectral compressibility at the metal-insulator transition of the quantum Hall effect [J].

Klesse, R ;

Metzler, M .

PHYSICAL REVIEW LETTERS, 1997, 79 (04) :721-724

[9] Dynamical scaling for critical states: Validity of Chalker's ansatz for strong fractality [J].

Kravtsov, V. E. ;

Ossipov, A. ;

Yevtushenko, O. M. ;

Cuevas, E. .

PHYSICAL REVIEW B, 2010, 82 (16)

[10]

Kravtsov V. E., 2010, HDB RANDOM MATRIX TH

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