  A perturbative model is studied for the tunneling of many-particle states
from the ground band to the first excited energy band, mimicking Landau-Zener
decay for ultracold, spinless atoms in quasi-one dimensional optical lattices
subjected to a tunable tilting force. The distributions of the computed
tunneling rates provide an independent and experimentally accessible signature
of the regular-chaotic transition in the strongly correlated many-body dynamics
of the ground band.
