The combination of the average projective phonon numbers δN∼ governed by U∼1α . The dashed lines correspond to the topological invariant ν₁/2 governed by U₁. (a) The combination of the average projective phonon numbers δN∼ as a function of the rotation angle θ₁ with t = 19, θ₂ = 3π/2 and |α| = 0.3. (b) The combination of the average projective phonon numbers δN∼ as a function of the step t with |α| = 0.3, θ₂ = 3π/2 and θ₁ = π/4. For the situation with (c), (d) dynamical disorder or (e), (f) decoherence, the solid lines indicate the ensemble average over 50 times of DTQWs with dynamical disorder or decoherence.