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Renormalization group analysis and quasicrystals. (English) Zbl 0789.58080
Albeverio, Sergio (ed.) et al., Ideas and methods in quantum and statistical physics. In memory of Raphael Hœgh-Krohn (1938-1988). Volume 2. Cambridge: Cambridge University Press. 118-148 (1992).
This is a review article on the application of the renormalization group methods for the study of Hamiltonian motions in a quasi-crystal. Topics covered are: (i) The Jacobi matrix associated with a Julia set which yields a new class of Hamiltonians with Cantor spectra, (ii) the Sierpinski lattice in a magnetic field, (iii) the Kohmoto model in one- dimensional quasi-crystals, (iv) quantal observable algebra using the cut and projection method of the Kohmoto model and (v) a brief description of higher dimensional lattices.
For the entire collection see [Zbl 0747.00053].

MSC:
58Z05 Applications of global analysis to the sciences
82B28 Renormalization group methods in equilibrium statistical mechanics
82D25 Statistical mechanical studies of crystals
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