Trapping problem on a line with a dichotomous disorder

We study the problem of random trapping on a linear chain when a random walker moves under the influence of a dichotomously disordered field to a neighboring site. The transition probability for moving to the right at each site is chosen with equal probability to be (1/2(1+E) or (1/2(1-E). We find that the long-time survival probability has the form S(t)∼A(c,E)t-b(c,E) where b(c,E)=2ln[1/(1-c)]/ln[1+E)/(1-E], c is the concentration of the traps, and A is a constant. For short times our theory suggests that the survival distribution is log-normally distributed, i.e., S(t)∼exp[-d(lnt)2]. These results are supported by numerical simulations.