We study the scattering of matter-waves from interacting bosons in a one-dimensional optical lattice, described by the Bose-Hubbard Hamiltonian. We derive analytically a formula for the inelastic cross section as a function of the atomic interaction
in the lattice, employing Bogoliubovs formalism for small condensate depletion. A linear decay of the inelastic cross section for weak interaction, independent of number of particles, condensate depletion and system size, is found.
We study quantum walks of many non-interacting particles on a beam splitter array, as a paradigmatic testing ground for the competition of single- and many-particle interference in a multi-mode system. We derive a general expression for multi-mode pa
rticle-number correlation functions, valid for bosons and fermions, and infer pronounced signatures of many-particle interferences in the counting statistics.
