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H. Schulz-Baldes, M. Zarrouati
Rigorous spectral analysis of the metal-insulator transition in
a limit-periodic potential
ABSTRACT. We consider the almost-periodic Jacobi matrices associated to
the real Julia sets of $f_\lambda(z)=z^2-\lambda$ for which $\lambda\in
[2,\infty)$ can be seen as the strength of the limit-periodic
coefficients. The typical local spectral exponent of their spectral
measures is shown to be a harmonic function in $\lambda$ decreasing
logarithmically from $1$ to $0$.