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On the asymptotic properties of quantum dynamics in the presence of a fractal spectrum. (English) Zbl 0817.47078

Summary: Asymptotic estimates for the dynamics induced in a separable Hilbert space by a discrete unitary group with a purely continuous spectrum are derived. They consist of upper and lower bounds for suitably defined exponents of growth. These bounds involve the capacity of the spectrum and the Hölder exponent of the spectral measure.

MSC:

47N50 Applications of operator theory in the physical sciences
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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