(a), (b) Time dependence of the mean energy. In (a), ℏ_eff = 0.01, from top to bottom solid lines correspond to δKmax=0.012 , 0.008, 0.005, and 0. In (b), δKmax=0.012 , from top to bottom solid lines correspond to ℏ_eff = 0.01, 0.02, 0.03, and 0.05. For comparison, red-dashed lines denote the classical mean energy with δKmax=0 . (c) Momentum distribution at the time t = 500 with δKmax=0.012 for ℏ_eff = 0.01 and 0.05, respectively. The parameters are K = 1.8 and L = π. Black curves denote the momentum distributions for the two-particle systems with m = 0.001, K₁ = 1.8, ε = 2, λ = 10, and L = π (same as in Fig. 1(b)).