Computer simulation of decay kinetics of solitons and polarons in linear chain lattices

The diffusion-limited collisional decay process of solitons and polarons excited in a linear chain lattice is simulated numerically. The dependence of the survival function on the initial density and lattice disorder is examined. In the uniform chain, if the initial density N0 is sufficiently low, the probability of solitons surviving at a time t agrees well with Torney and McConnellʹs solution S(ζ)=exp(8ζ)erfc(8ζ)1/2, ζ=N02Dt, for the unimolecular chemical reaction in a continuous medium, where D is the diffusion constant; the lattice effect appears with increasing N0 as the slowing down of the initial decay. The survival probability of polarons is also given by a universal function S(ζ)=(1+33ζ)−1/4 within errors of ±2%. As the lattice disorder evolves, S(ζ) transforms into the Kohlrausch law S(ζ) = exp-(ζ/ζ0)β, 0 < β < 1, for both solitons and polarons, consistent with the experiment for long-lived photoexcited solitons in an MX chain compound.