Abstract
The unusual phenomena occurring in the wave propagation in almost-periodic structures — both classical and quantum — are studied in this paper. Focusing our attention on structures with spectral measures in the family of disconnected iterated function systems, we describe and characterize the concept of “quantum intermittency”. This theory shows that the nontrivial renormalization properties of the set of orthogonal polynomials associated with these systems are the origin of such “intermittency”, and leads to a new determination of the exponents of the asymptotic growth of the moments of the position operator.
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