Fluctuation asymptotics of hopping quenching in disordered systems.

Abstract

The impurity quenching of incoherent excitation accelerated by resonance migration in solid solutions is studied. It is shown that a lower bound for the survival probability N(t) is established by so-called encounter theory, which is linear in the quencher concentration and predicts an exponential decay at the end of the migration-accelerated stage following a short static decay. Another lower bound, which is the probability of not leaving the site where the excitation was initially created, decays much more slowly at the very end of a process. The crossover point of these lower bounds establishes an upper time boundary ${\mathit{t}}_{\mathit{f}}$ for binary approximation. The real quenching initially well described by binary-encounter theory is completed by the ``fluctuation asymptotics'' of quenching, which is multiparticle in principle. In the hopping quenching limit, the continuous-time random-walk equation is used to find the starting point ${\mathit{t}}_{\mathit{f}}$ of the fluctuation stage and the share of excitations that have survived at that time N(${\mathit{t}}_{\mathit{f}}$). When migration is fast enough the latter is shown to be small, and the binary description of preceding stages proves to be good. However, with a decrease of the donor concentration, an intermediate migration-accelerated stage is ousted by multiparticle static quenching from one side and the fluctuation asymptotics from another.