ELECTRONIC SPECTRAL AND WAVE-FUNCTION PROPERTIES OF ONE-DIMENSIONAL QUASI-PERIODIC SYSTEMS - A SCALING APPROACH

Here V is a function of period 1 and omega is irrational. For the Fibonacci model, V takes only two values (it is constant except for discontinuities) and the spectrum is purely singular continuous (critical wavefunctions). When V is a smooth function, the spectrum is purely absolutely continuous (extended wavefunctions) for lambda small and purely dense point (localized wavefunctions) for lambda large. For an intermediate lambda, the spectrum is a mixture of absolutely continuous parts and dense point parts which are separated by a finite number of mobility edges. There is no singular continuous part. (An exception is the Harper model V (x) = cos(2pi-x), where the spectrum is always pure and the singular continuous one appears at lambda = 2.)