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Fibonacci, Koch, and Penrose Structures: Spectrum of Finite Subsystems in Three‐Dimensional Space
Author(s) -
de Prunelé E.,
Bouju X.
Publication year - 2001
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/(sici)1521-3951(200105)225:1<95::aid-pssb95>3.0.co;2-s
Subject(s) - fibonacci number , aperiodic graph , eigenvalues and eigenvectors , space (punctuation) , penrose tiling , basis (linear algebra) , coupling (piping) , spectrum (functional analysis) , physics , mathematics , mathematical physics , quantum mechanics , theoretical physics , quasicrystal , pure mathematics , geometry , combinatorics , computer science , mechanical engineering , engineering , operating system
The electronic eigenvalues and eigenstates of finite Fibonacci, Koch, and Penrose structures are studied on the basis of a recently proposed three‐dimensional solvable model [J. Phys. A 30 , 7831 (1997)]. This model allows to take into account explicitly the geometry of the aperiodic structures in three‐dimensional space and involves no assumption such as the coupling of nearest‐neighbouring atoms only.