Survival probability in a quantum walk on a one-dimensional lattice with partially absorbing traps

Abstract

Time dependence of the survival probability in a one dimensional lattice with randomly distributed and partial absorbing traps is analyzed as a function of concentration and absorption probability of the traps. The short and long time behaviors of the non-interacting quantum walks are identified with stretched exponentials. Dynamical scaling laws of the short and long time regimes as well as the crossover time between them are characterized. It is found that the short time behavior is more sensitive to the absorption probability and the crossover takes longer time for more transparent traps. Moreover, the stretching exponents increase with the transparency of the traps.