  We study a model for ultracold, spinless atoms in quasi-one dimensional
optical lattices and subjected to a tunable tilting force. Statistical tests
are employed to quantitatively characterize the spectrum of the Floquet-Bloch
operator of the system along the transition from the regular to the quantum
chaotic regime. Moreover, we perturbatively include the coupling of the
one-band model to the second energy band. This allows us to study the
Landau-Zener interband tunneling within a truly many-body description of
ultracold atoms. The distributions of the computed tunneling rates provide an
independent and experimentally accessible signature of the regular-chaotic
transition.
