(a) Time dependence of the classical (red line) mean energy and quantum mean energy (black lines) of particle 1. From top to bottom, black solid lines correspond to ℏ_eff = 0.01, 0.02, 0.03, 0.04, and 0.05, respectively. The parameters are K₁ = 1.8, K₂ = 0, m = 0.001, ε = 2, λ = 10, and L = π. For comparison, the dashed line (in blue) denotes the quantum mean energy of the unperturbed case, i.e., ε = 0 with K = 1.8 and ℏ_eff = 0.01. (b) Momentum distribution at the time t = 500 with ℏ_eff = 0.01 (blue curve) and 0.05 (black curve). Dash-dotted line (in red) indicates the fitting function of the Gaussian form |ψ₁(p)|²∝ e^−p2/ζ. Dashed line (in red) denotes the exponential fitting |ψ₁(p)|²∝ e^−|p|/ξ.