Assignment Solutions in Physics, Physical Chemistry, Astrophysics, Computer Simulation, and Numerical Calculation

Velocity Correlation Function

Question: Consider the Langevin equation

with < f (t) >= 0.

a) Calculate the velocity correlation function < v(0)v(t) > at all times. This function shows how velocity is correlated with its initial value. What are the values of this function at t=0 and t → ∞?

b) Calculate

Solution: a) By multiplying Langevin equation by exp(−t ξ/m) , we get,