# 8.4 Diffusion by NEMD

To determine the diffusion constant Ciccotti et al. [J. Stat. Phys. 21(1979)1] suggest the following Hamiltonian non-equilibrium method:
Let
 (8.43)

where for even/odd numbered particles is a color charge'' coupling to the applied color field'' .

In other words, particles are drawn in opposite directions depending on their number; otherwise, they are completely identical.

Keeping constant we have
 (8.44)

where is the color current''.

Again, the external field does work on the system, heating it:
 (8.45)

The heating may once more be avoided by Gaussian terms in the eqs. of motion which now read, in 2 dimensions,
 (8.46) (8.47) (8.48) (8.49)

In this way a color conductivity''
 (8.50)

may be evaluated. Applying Linear Response Theory one may show that is closely related to the diffusion constant:
 (8.51)

F. J. Vesely / University of Vienna