Transport of excitations in disordered systems: Self-consistent density resummation

New self-consistent equations for the transport of excitations in disordered systems are derived based on a resummation procedure of the density expansion. Both local-time [partial-time-ordering prescription (POP)] and convolution-type [chronological-time-ordering prescription] equations are explored. Application is made to a system consisting of a random mixture of donors and traps with a general type of transfer rate $W(r)$. We calculate the probability of remaining in the original site G₀(t) as well as the second moment of the distribution of excitations 〈r²(t)〉. The POP equations reduce to the exact Forster solution for G₀(t) in the case of traps only. We analyze the long-time behavior of G₀(t) and its dependence on $W(r)$. We find a percolation-type transition when $W(r)$ has a cutoff [i.e., $W(r)=0$ for r>r₀] but in all other cases the system is diffusive at long times [G₀(t) vanishes and 〈r²(t)〉 diverges linearly in time].