Fig. 1. Diffusion speed versus phase φ when t=20 and d=0.5

Fig. 2. Probability distributions of walker's position under different conditions. (a) d=0.2, φ=0; (a) d=0.2, φ=π/4; (c) d=0.5, φ=0; (d) d=0.5, φ=π/4; (e) d=0.8, φ=0; (f) d=0.8, φ=π/4

Fig. 3. Variance of position versus number of steps under different conditions. (a) No phase added; (b) d=0.2; (c) d=0.5; (d) d=0.8