Lévy Ratchet — Asymmetric Anomalous Drift

Particles performing Lévy flights (heavy-tailed jumps, α-stable distributions) in a sawtooth potential exhibit net drift even without bias. The asymmetric potential rectifies the long jumps to produce directed transport.

Controls

Mean drift:
MSD exponent:
Step: 0
Dots: particles.
Sawtooth: ratchet potential.
α=2: Gaussian (no net drift).
α<2: Lévy → net drift.
Asymmetry a: slope ratio.