The difference of the average projective phonon numbers ΔN governed by U1α . The dashed lines correspond to the topological invariant ν₁/2 of our DTQW governed by U₁. (a), (b) The difference of the average projective phonon numbers ΔN without dynamical disorder and decoherence, as functions of the rotation angle θ₁ and the step t with θ₁ = π/4, the rotation angle θ₂ is fixed at 3π/2. The solid (dash-dotted) lines indicate |α| = 1.5 (0.5). (c)–(f) The difference of the average projective phonon numbers ΔN with (c), (d) dynamical disorder or (e), (f) decoherence, as functions of the rotation angle θ₁ or the step t with θ₁ = π/4, the rotation angle θ₂ is fixed at 3π/2 and |α| = 1.5. The solid lines indicate the ensemble average over 50 times of DTQWs with dynamical disorder or decoherence.