(a) The mean diffusion velocity along the x-axis by varying the quasi-disorder Γ (Γ = ε₂ = ε₄, ε₁ = ε₃ = 1) for different interaction strength g and lattice depth V0′ . (b) Time evolution of the mean-square position along the x-axis upon released from the harmonic trap in periodic (Γ = 0) and quasi-periodic (Γ = 0.5, 1) lattices with V0′=−2 and g = 10. Other parameters used in this figure are ωr′=0.08 and Ω = 0.