Driven Brownian Ratchet

Asymmetric sawtooth potential + noise → net directed current. No net force required — broken spatial symmetry rectifies fluctuations.

Noise D = 0.40

Asymmetry α = 0.25

Drive F = 0.00

N particles = 30

Mean velocity: 0.000

Overdamped Langevin: ẋ = −V'(x) + F + √(2D)·ξ(t), ξ Gaussian white noise. Sawtooth V(x): slow rise over α·L, steep fall over (1−α)·L per period. Spatial asymmetry + noise → rectified motion even at F=0 (flashing or tilting ratchet).