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Resonances for open quantum maps and a fractal uncertainty principle. (English) Zbl 1372.81101
Open quantum maps are useful models in the study of scattering phenomena and in particular scattering resonances. This paper investigates eigenvalues for a family of open quantum maps known as quantum open Baker’s maps. The corresponding trapped orbits form Cantor sets. The combinatorial and number theoretic properties of these sets make it possible to prove results on spectral gaps that lie well beyond what is known for other models. A fractal Weyl upper bound also is given and numerical results are provided.

MSC:
81S22 Open systems, reduced dynamics, master equations, decoherence
28A80 Fractals
81U05 \(2\)-body potential quantum scattering theory
35P05 General topics in linear spectral theory for PDEs
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