Langevin Brownian Particle: Ballistic → Diffusive Transition

Adjust friction γ and temperature T. The left panel shows the particle trajectory; the right panel shows the mean-squared displacement (MSD) on a log-log plot. The slope transitions from 2 (ballistic, ∝ t²) to 1 (diffusive, ∝ t).

Particle trajectory (last 500 steps)

MSD ⟨Δx²⟩ vs t (log-log). Dashed lines: t² (ballistic) and t (diffusive).

D = kBT/γ = 0.50 | Relaxation time τ = m/γ = 0.50