Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)In this work, we follow the time evolution of an initially localized one-electron wavepacket in a random ladder model with correlated diagonal disorder. Weak localization of the eigenstates is anticipated for antisymmetric cross-correlations with every base pair having the same average energy. We show that the wavepacket width develops damped Rabi-like oscillations after reaching the ladder's borders. The Rabi-like oscillations are shown to originate from the interference between neighboring energy eigenstates, while its damping is associated with a destructive interference due to the random scattering in the underlying random potential. The typical damping time t(d) is estimated as a function of the ladder size N and shown to increase as t(d)proportional to N-z with z = 0.62(4). The strong localization in the absence of antisymmetric cross-correlations suppresses the oscillations. (c) 2013 Elsevier B.V. All rights reserved.54157161Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)FINEPAlagoas state research agency FAPEALConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)