Multifractal states in self-consistent theory of localization: analytical solution

2016/10/03 by B. L. Altshuler, L. B. Ioffe, Altshuler, B. L. +3
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Fractal and DNA sequence analysis #Theoretical and Computational Physics #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.1610.00758

Abstract

We consider disordered tight-binding models which Green's functions obey the self-consistent cavity equations . Based on these equations and the replica representation, we derive an analytical expression for the fractal dimension D₁ that distinguishes between the extended ergodic, D₁=1, and extended non-ergodic (multifractal), 0

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