We report the first numeric experiments on diffusion in living polymer
s (polymers that can break and recombine reversibly, and are character
ized by an exponential molecular weight distribution). In the simulati
on we use a modification of the bond fluctuation model which is known
to reproduce the correct Rouse dynamics of polymer chains. The diffusi
on coefficient D reveals a Rouse-type behaviour D proportional to 1/L,
where L is the average chain length of the polydisperse system. We al
so find a D proportional to exp[-V/2k(B)T] dependence on the bond ener
gy V, whereas at constant temperature the diffusion coefficient turns
out to be inversely proportional, D proportional to rho(-1), to the mo
nomer density of the system rho in agreement with mean-field descripti
on of living polymers.