Wave propagation in almost-periodic structures. (English) Zbl 0925.58041

Summary: 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 non-trivial 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.


37A99 Ergodic theory
28A80 Fractals
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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