Renormalization group analysis and quasicrystals. (English) Zbl 0789.58080

Bellissard, J.

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].

Reviewer: C.S.Sharma (London)

MSC:

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

Keywords:

renormalization group methods; Hamiltonian motions; Jacobi matrix; Julia set; Sierpinski lattice; magnetic field; Kohmoto model; quasi-crystals