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I'm studying quantum Brownian motion right now and I need to see that the (classical) Langevin equation for a Brownian particle is equivalent to the Fokker-Planck equation for the phase-space distribution function of the same particle.

Does anyone know where I can find such a derivation? I've been looking all over the internet for it but usually they start with a Langevin equation containging only first derivatives (that is the have excluded the possible outer potential felt by the particle).

I need the derivation for the case where i have a Langevin equation of the type:

m \ddot x(t) + \gamma \dot x(t) + V(x(t)) = F(t)

(written in LaTeX syntax).

I would be very grateful for help!

Alternatively, since I have the derivation for the Langevin equation starting with a Lagrangian for a particle interacting linearly with a bath of harmonic oscillators (initially in thermal equilibrium), I could also accept a derviation of the Fokker-Planck equation starting with the same assumptions.

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# From Langevin to Fokker-Planck

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