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Quantum Intermittency in Almost-Periodic Lattice Systems Derived from their Spectral Properties

Hamiltonian tridiagonal matrices characterized by multi-fractal spectral measures in the family of Iterated Function Systems can be constructed by a recursive technique here described. We prove that these Hamiltonians are almost-periodic. They are suited to describe quantum lattice systems with nearest neighbours coupling, as well as chains of linear classical oscillators, and electrical transmission lines. We investigate numerically and theoretically the time dynamics of the systems so constructed. We derive a relation linking the long-time, power-law behaviour of the moments of the position operator, expressed by a scaling function $β$ of the moment order $α$, and spectral multi-fractal dimensions, D_q, via $β(α) = D_{1-α}$. We show cases in which this relation is exact, and cases where it is only approximate, unveiling the reasons for the discrepancies.