Description of Simulation
We consider one atom at the origin, initially in the state
s', surrounded by a gas of N randomly placed
s atoms. This system is described by the equations
Here a0 is the amplitude of the initial
state, while ck is the amplitude of the
state in which the atom at the origin is in state p'
and the atom at position rk is in state
p, but all the other atoms remain in state s.
The potentials Vk and Ukl
are of the dipole-dipole forms
,
where µ and µ' are the dipole
matrix elements connecting the s and p states,
and the s' and p' states, respectively. The
simulation is carried out by solving the
N + 1 coupled differential equations
for many random distributions of the atoms, and then
averaging the results.