One-dimensional quantum transport in the presence of traps

A study is made of the survival probability P(t) for a quantum particle moving coherently on an ordered one-dimensional chain containing randomly placed irreversible traps in concentration q. We consider two separate models of the trapping process, focusing on the long-time limit of each. In the first model, intended to describe substitutional traps, the trapping impurities act as disruptive absorbing barriers which prevent further motion along the chain. For this model it is shown that -ln[P(t)]∼$t^{1/4}$. The second model is intended to describe interstitial trapping impurities which do not disrupt the transport. It is argued for this case that Anderson localization of the quasiparticle wave functions will occur in the otherwise ordered chain as a result of the disorder introduced by the trapping impurities. In addition, it is suggested that the asymptotic decay of P(t) will be dominated by slowly decaying long-wavelength modes associated with asymptotically large segments of the chain which are free of traps. Our analysis predicts that the asymptotic decay will be of the same form as that which obtains in the substitutional model. Numerical results that we have performed support this prediction.