Power spectrum for critical statistics: A novel spectral characterization of the Anderson transition

Details Power spectrum for critical statistics: A novel spectral characterization of the Anderson transition Power spectrum for critical statistics: A novel spectral characterization of the Anderson transition

2005-10-24

arxiv.org/abs/cond-mat/0510645v1

Phys.Rev. E73 (2006) 026213

Physics

Condensed Matter

Disordered Systems and Neural Networks

9 pages, 4 figures

Scientific paper

10.1103/PhysRevE.73.026213

We examine the power spectrum of the energy level fluctuations of a family of critical power-law random banded matrices with properties similar to those of a disordered conductor at the Anderson transition. It is shown both analytically and numerically that the Anderson transition is characterized by a power spectrum which presents $1/f^2$ noise for small frequencies but $1/f$ noise for larger frequencies. The analysis of the transition region between these two power-law limits gives an accurate estimation of the Thouless energy of the system. Finally we discuss under what circumstances these findings may be relevant in the context of non-random Hamiltonians.

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