ELECTRONIC DYNAMICS IN AN INCOMMENSURATE SYSTEM

The electronic dynamics of an incommensurate system have been studied with site potentials Vn=λtanh［Acos(2πσn)］/tahnA, where σ=(5-1)/2. By analyzing the wave function, we find the extended eigenstates are similar to the Bloch waves, and critical states occur in some Hamiltonian parameter regions. Much attention is paid to the long-time behavior of the autocorrelation function C(t) and mean square displacement d(t). When all states in the system become extended, C(t)～t-1 and d(t)～t1. In the regime with absolute localized states, C(t)～t0 and d(t)～t0. Between these two extremes, there exists a complex phase regime in which extended states, critical states and localized states coexist, and the behavior of C(t) is related to the initial site, but with d(t)～t1. Moreover, the relation between C(t) and the local spectral probability R(l) have been studied.