Abstract
We show the localization transition and its influence on two dynamical processes of an extended Aubry–André–Harper model with incommensurate on-site and hopping potentials. After specifying an extended Aubry–André–Harper model, we check the localization transition for all the eigenstates and eigenenergy band splitting behavior versus a system parameter. To check the influence of localization transition on dynamical processes, firstly, the slowly pumping of edge states are examined. The adiabatic pumping is suppressed in the localized region. Then by quantum Lyapunov control method in terms of different control Hamiltonians, we prepare an edge-localized state in the nonlocal region. The control effect is suppressed in the localized region compared to that in the nonlocal region. In the dynamical processes, the system acts as conductor for the excitation in the nonlocal region and insulator in the localized region. Then we adopt the occupation imbalance between even and odd sites and entropy to indicate the localization transition further. Finally, the experimental schemes based on cold atoms trapped in quasiperiodic optical lattice and coupled optical waveguide arrays are suggested.
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