Renormalization of wave function fluctuations for a generalized Harper equation
A renormalization analysis is presented for a generalized Harper equation
(1 + Î± cos(2Ï€(Ï‰(i + 1/2) + Ï†)))Ïˆi+1 + (1 + Î± cos(2Ï€(Ï‰(i âˆ’ 1/2) + Ï†)))Ïˆiâˆ’1
+2Î» cos(2Ï€(iÏ‰ + Ï†))Ïˆi = EÏˆi. (0.1)
For values of the parameter Ï‰ having periodic continued-fraction expansion,
we construct the periodic orbits of the renormalization strange sets in function
space that govern the wave function fluctuations of the solutions of the
generalized Harper equation in the strong-coupling limit Î»â†’âˆž.
For values of Ï‰ with non-periodic continued fraction expansions, we make
some conjectures based on work of Mestel and Osbaldestin on the likely
structure of the renormalization strange set.