  We study the spreading of a quantum particle placed in a single site of a
lattice or binary tree with the Hamiltonian permitting particle number changes.
We show that the particle number-changing interactions accelerate the spreading
beyond the ballistic expansion limit by inducing off-resonant Rabi oscillations
between states of different numbers of particles. We consider the effect of
perturbative number-changing couplings on Anderson localization in
one-dimensional disordered lattices and show that they lead to decrease of
localization. The effect of these couplings is shown to be larger at larger
disorder strength, which is a consequence of the disorder-induced broadening of
the particle dispersion bands.
