Electronic dynamics in an incommensurate system

The electronic dynamics of an incommensurate system have been studied with site potentials V-n, = lambda tanh[ Acos(2 pi sigma n)]/tahnA, where sigma = ( root 5-1)/2. By analyzing the wave function, we find the extended eigen states are similar to the: Bloch waves, and critical states occur in some H amiltonian parameter-regions. Much attention is paid to the long-time behav ior of the autocorrelation function C(t) and mean square displacement d(t). When all states in the system become extended, C(t) similar to t(-1) and d (t) similar to t(1). In the regime with absolute localized states, C(t) sim ilar to t(0) and d(t) similar to t(0) Between these two extremes, there exi sts a complex phase regime in which extended states, critical states and lo calized states coexist, and the behavior of C(t) is related to the initial site, but with d(t) similar to t(1). Moreover, the relation between C(t) an d the local spectral probability R(l) have been studied.