Flashing Ratchet

Asymmetric potential + Brownian noise = directed transport without net force

γẋ = −∂V(x)/∂x + √(2γk_BT)·η(t) | V flashes ON/OFF at rate ω
Sawtooth: V(x) = V₀·[x/a − floor(x/a)] for 0≤x/a≤α, broken symmetry α≠0.5

Noise temperature k_BT/V₀ = 0.30

Switching rate ω (on/off per τ) = 2.0

Asymmetry α (peak position) = 0.25

Barrier height V₀ = 1.0

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Mean velocity

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Mean position

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Potential state