2003/03/12 by J. Vidal, Julien Vidal, N. Destainville +3 · 11 citations
Biochemistry, Genetics and Molecular Biology · Materials Science · Mathematics · Physics and Astronomy · #Codimension #Degenerate energy levels #Diffusion and Search Dynamics #Exponent #Limit (mathematics) #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantum mechanics #Quasicrystal Structures and Properties #Quasiperiodic function #Quasiperiodicity #Statistical physics #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevb.68.172202
published in Physical review. B, Condensed matter 68(17) (American Physical Society) · 4 pages, 5 EPS figures
arxiv created 2003/03/12 · openalex publication_date 2003/11/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We analyze the spreading of wave packets in two-dimensional quasiperiodic and random tilings as a function of their codimension, i.e., of their topological complexity. In the quasiperiodic case, we show that the diffusion exponent that characterizes the propagation decreases when the codimension increases and goes to 1/2 in the high codimension limit. By contrast, the exponent for the random tilings is independent of their codimension and also equals 1/2. This shows that, in high codimension, the quasiperiodicity is irrelevant and that the topological disorder leads in every case, to a diffusive regime, at least in the time scale investigated here.