where 
is the mass of each ion, 
its charge and 
the
applied electric field.
Note that in this equation, the momenta are chosen so that 
ve species
is carrying 
of the current, where 
is the mass of the
negative and positive ion respectively. In the particular case of 
,
which we shall discuss henceforth, each species carries half the current. In a
real electrical system, the forces 
must be sums of Coulomb terms
(
), which is effectively of
infinite range, so there will be significant error involved in modelling it
with the small systems available with computer simulations. There is a
technique for resumming the electrical forces to take into account the
screening effect [Allen and Tildesley
[1987]]
,
but since at this stage we are interested in the feasibility of such
calculations, rather realistic values, we take
a simpler approach of using a short range force, such as the Lennard-Jones
force. We call this colour conductivity to
distinguish it from electrical conductivity, because we can consider that each
molecule has a colour label which interacts with the colour field, but that
the Hamiltonian is colour blind. A number of authors have studied this system
[Evans and Morriss
[1985], Evans et al.
[1983], Erpenbeck
[1987]]
.