Uncertainties of clock and shift operators for an electron in one-dimensional nonuniform lattice systems

Gong Long-Yan^{1, 2, 3, †}, Ding You-Gen², Deng Yong-Qiang²

(color online) For the slowly varying potential model, (a) ΔU², (b) ΔV², (c) U_r, (d) LB, and (e) IPR as functions of eigenenergies E_β, respectively. Here, λ = 1.0t, πα = 0.2, and υ = 0.7; the vertical dashed lines are for the functions and , respectively; the horizontal dashed line in panel (c) is for U_r = 0; lattice sizes d = 1000, 2000, and 10000, respectively. Inset in panel (c): partial enlarger for E_β near .