The Langevin equation for a particle in 1 dimension in an external potential V (x) is:...

The Langevin equation for a particle in 1 dimension in an external potential V (x) is: mx'' =-(dV(x)/dx)-ξx'+F(t), where ξ is the friction constant, and F(t) is the random force.Take V (x) to be harmonic: V (x) = (m/2)ω^2x^2 .Find the general solution x(t) for arbitrary initial conditions and calculate the equilibrium time correlation function C(t) = <x(t)x(0)>.

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genius_generous answered 1 year ago

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