Kramers Rate: Stochastic Switching

Kramers' escape rate theory: a particle in a double-well potential escapes over the barrier at rate k ∝ exp(−ΔV/D), where D is noise intensity. Watch the particle switch wells and measure the mean first-passage time.

ẋ = −V'(x) + √(2D)·ξ(t)
V(x) = x⁴/4 − x²/2 − Fx
k ≈ (ω₀ω_b/2π)e^(−ΔV/D)
Kramers rate k:
Mean MFPT theory:
Mean MFPT measured:
Switches (left→right): 0
Switches (right→left): 0