# Langevin dynamics random force term generation algorithm

1. Aug 11, 2008

### iibewegung

Hi,

Can anyone tell me an algorithm to generate the stationary Gaussian distribution R(t) with

$$\langle R(t) \rangle = 0$$ (zero mean)
$$\langle R(t) R(t')^{T} \rangle = A \delta(t-t')$$, $$A = 2 \gamma k_B T m$$ (autocorrelation)

?

What I just wrote is from the Wikipedia article "Langevin dynamics"
and R(t) belongs to the simple Langevin equation
$$F(x) = m \ddot{x} = -\nabla U(x) - \gamma m \dot{x} + R(t)$$

Last edited: Aug 11, 2008
2. Feb 23, 2009

### jwallace

I have been looking for the same code. It is not exactly trivial. I found some code in the following book
"The Molecular Dynamics of Liquid Crystals,by G. R. Luckhurst, C. A. Veracini"
I have been looking for a DJVU copy of this book but havent found one.

3. Dec 4, 2009