ENERGY-SPECTRUM AND THE CRITICAL WAVE-FUNCTIONS OF THE QUASI-PERIODICHARPER EQUATION - THE SILVER MEAN CASE

The one-dimentional quasiperiodic tight-binding model is -psi(n+1)-psi (n-1)+lamdaV(nomega)psi(n)=Epsi(n), where omega is an irrational numbe r and Vis a periodic function, i.e., V(x+1)=V(x). In the Harper model V(nomega)=cos(2pinomega), all the states are critical at the critical coupling lambda(c)=2. The critical properties of the spectrum and the wavefunctions for omega = square-root 2 - 1 (the inverse of the silver mean) are numerically studied by the scaling and multifractal methods . The results are compared with the golden mean case omega=(square-roo t 5-1)/2. Some universal properties are proposed.