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

Abstract

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.

9 pages, 4 figures

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• Theoretical derivation of 1/f noise in quantum chaos
• The Anderson transition in quantum chaos
• Intermediate statistics in quantum maps
• Virial expansion for almost diagonal random matrices
• Multifractality of Hamiltonians with power-law transfer terms
• Classical singularities and Semi-Poisson statistics in quantum chaos and disordered systems
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• Anderson Transitions
• Power Spectrum of Long Eigenlevel Sequences in Quantum Chaotic Systems
• Boundary multifractality in critical 1D systems with long-range hopping
• Nonperturbative theory of power spectrum in complex systems
• Many-Body Localization in a finite-range Sachdev-Ye-Kitaev model
• Anderson localization transition with long-ranged hoppings : analysis of the strong multifractality regime in terms of weighted Levy sums
• Long-range level correlations in quantum systems with finite Hilbert space dimension
• Statistics of the two-point transmission at Anderson localization transitions
• A critical Dyson hierarchical model for the Anderson localization transition
• Spectral analysis of molecular resonances in erbium isotopes: Are they close to semi-Poisson?
• Approaching Thouless Energy and Griffiths Regime in Random Spin Systems By Singular Value Decomposition
• Universality of a family of Random Matrix Ensembles with logarithmic soft-confinement potentials
• Statistical properties of two-particle transmission at Anderson transition