Issue |
EPL
Volume 98, Number 3, May 2012
|
|
---|---|---|
Article Number | 37006 | |
Number of page(s) | 6 | |
Section | Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties | |
DOI | https://doi.org/10.1209/0295-5075/98/37006 | |
Published online | 14 May 2012 |
Multifractal dimensions for critical random matrix ensembles
1
Instituto de Física, Benemérita Universidad Autónoma de Puebla - Apartado Postal J-48, Puebla 72570, Mexico
2
Elméleti Fizika Tanszék, Fizikai Intézet, Budapesti Műszaki és Gazdaságtudományi Egyetem H-1521 Budapest, Hungary, EU
3
Fachbereich Physik und Wissenschaftliches Zentrum für Materialwissenschaften, Philipps Universität Marburg D-35032 Marburg, Germany, EU
Received:
30
January
2012
Accepted:
13
April
2012
Based on heuristic arguments we conjecture that an intimate relation exists between the eigenfunction multifractal dimensions Dq of the eigenstates of critical random matrix ensembles Dq′≈qDq[q′ +(q− q′ )Dq]−1, 1⩽q⩽2. We verify this relation by extensive numerical calculations. We also demonstrate that the level compressibility χ describing level correlations can be related to Dq in a unified way as Dq=(1− χ)[1+(q−1)χ]−1, thus generalizing existing relations with relevance to the disorder-driven Anderson transition.
PACS: 71.30.+h – Metal-insulator transitions and other electronic transitions / 05.45.Df – Fractals
© EPLA, 2012
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