Quantum walks assisted by particle number fluctuations

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.