Fibonacci Quasiperiodic Chain — Tight-Binding Spectrum

Fibonacci quasicrystal — The chain is built by the substitution rule A→AB, B→A, producing lengths 1,1,2,3,5,8,13,… (Fibonacci numbers). Unlike periodic crystals, the spectrum is a Cantor set of measure zero in the thermodynamic limit — infinitely fragmented with self-similar gaps. The tight-binding Hamiltonian H_ij = V_iδ_ij + t_ijδ_|i-j|,1 alternates hopping amplitudes t_A/t_B following the Fibonacci word. The integrated density of states (IDS) is a devil's staircase. The ratio t_A/t_B = φ (golden ratio ≈1.618) is the self-similar fixed point.

QuasicrystalCantor spectrumSelf-similarityTight-binding1D Schrödinger