We consider the dynamics of the quantum XY chain with disorder under thegeneral assumption that the expectation of the eigenfunction correlator of theassociated one-particle Hamiltonian satisfies a decay estimate typical ofAnderson localization. We show that, starting from a broad class of productinitial states, entanglement remains bounded for all times. For the XX chain,we also derive bounds on the particle transport which, in particular, show thatthe density profile of initial states that consist of fully occupied and emptyintervals, only have significant dynamics near the edges of those intervals,uniformly for all times.
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