The quantum dynamics of an electron in a one-dimensional Thue-Morse lattice is studied. The asymptotic long-time behavior of the electronic wave packet is shown to be characterized by a superdiffusive movement with dynamic indices intermediate between...
The quantum dynamics of an electron in a one-dimensional Thue-Morse lattice is studied. The asymptotic long-time behavior of the electronic wave packet is shown to be characterized by a superdiffusive movement with dynamic indices intermediate between those of the periodic and the Fibonacci lattices. It is also found that the dependence of the dynamic index on the system parameters is much weaker than that of the Fibonacci lattice. Our findings strongly reflect the peculiar electronic properties of the Thue-Morse lattice, the electronic eigenstates are extended while the energy spectrum is singular continuous. The results obtained using alternative measures characterizing the dynamics of the wave packet are also presented.