Non-commutative Models for Quasicrystals

  • P. Kramer
  • J. Garcia-Escudero
Conference paper
Part of the Centre de Physique des Houches book series (LHWINTER, volume 3)


A powerful approach to quasicrystals arises from the use of n-dimensional crystallography: Given a non-crystallographic point group H in R 3, look for the lattice Γ of minimal dimension n which has H as (part of) its point group. The n-dimensional representation of H must be reducible and contain a 3D representation. Split R n into this representation space R 3 and its orthogonal complement, construct discrete quasiperiodic patterns by projection from the lattice to R 3 and use the orthogonal complement for windows and for coding. Periodicity and tranlational symmetry in R 3 are absent by construction. This scheme allows to treat diffraction properties by lifting the Fourier coefficients to the reciprocal lattice Γ R .


Point Symmetry Coxeter Group Monoid Structure Formal Grammar Input Tape 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • P. Kramer
    • 1
  • J. Garcia-Escudero
    • 2
  1. 1.Institut für Theoretische PhysikUniversität TübingenTübingenGermany
  2. 2.Departamento de FisicaUniversidad de OviedoOviedoSpain

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