Are the phase in the Anderson model long-range correlated?

Jan W. Kantelhardt; Richard Berkovits; Shlomo Havlin; Armin Bunde

doi:10.1016/s0378-4371(98)00631-1

Are the phase in the Anderson model long-range correlated?

Jan W. Kantelhardt
, Richard Berkovits
, Shlomo Havlin
, Armin Bunde

Department of Physics - at Bar-Ilan University

Justus Liebig University Giessen
Bar-Ilan University

Research output: Contribution to journal › Conference article › peer-review

40 Scopus citations

Abstract

We investigate the local cumulative phases at single sites of the lattice for time-dependent wave functions in the Anderson model in d = 2 and 3. In addition to a local linear trend, the phases exhibit some fluctuations. We study the time correlations of these fluctuations using detrended fluctuation analysis. Our results suggest that the phase fluctuations are long-range correlated, decaying as a power law with time. It seems that the exponent depends on the degree of disorder. In d = 3, close to the critical disorder w_c = 16.5, the correlation exponent exhibits a maximum value of α ≈ 0.6 which is significantly above random fluctuations (α = 0.5).

Original language	English
Pages (from-to)	461-464
Number of pages	4
Journal	Physica A: Statistical Mechanics and its Applications
Volume	266
Issue number	1-4
DOIs	https://doi.org/10.1016/s0378-4371(98)00631-1
State	Published - 15 Apr 1999
Event	Proceedings of the 1998 International Conference on Percolation and Disordered Systems: Theory and Applications - Giessen, Ger Duration: 14 Jul 1998 → 17 Jul 1998

Bibliographical note

Funding Information:
We thank the Deutsche Forschungsgemeinschaft for financial support.

Funding

We thank the Deutsche Forschungsgemeinschaft for financial support.

Funders
Deutsche Forschungsgemeinschaft

Access to Document

10.1016/s0378-4371(98)00631-1

Cite this

@article{a9977a055ef04ff380487738f9397b63,

title = "Are the phase in the Anderson model long-range correlated?",

abstract = "We investigate the local cumulative phases at single sites of the lattice for time-dependent wave functions in the Anderson model in d = 2 and 3. In addition to a local linear trend, the phases exhibit some fluctuations. We study the time correlations of these fluctuations using detrended fluctuation analysis. Our results suggest that the phase fluctuations are long-range correlated, decaying as a power law with time. It seems that the exponent depends on the degree of disorder. In d = 3, close to the critical disorder wc = 16.5, the correlation exponent exhibits a maximum value of α ≈ 0.6 which is significantly above random fluctuations (α = 0.5).",

author = "Kantelhardt, \{Jan W.\} and Richard Berkovits and Shlomo Havlin and Armin Bunde",

note = "Funding Information: We thank the Deutsche Forschungsgemeinschaft for financial support. ; Proceedings of the 1998 International Conference on Percolation and Disordered Systems: Theory and Applications ; Conference date: 14-07-1998 Through 17-07-1998",

year = "1999",

month = apr,

day = "15",

doi = "10.1016/s0378-4371(98)00631-1",

language = "אנגלית",

volume = "266",

pages = "461--464",

journal = "Physica A: Statistical Mechanics and its Applications",

issn = "0378-4371",