A two-band Bose-Hubbard model for many-body resonant tunneling in the   Wannier-Stark system
  We study an experimentally realizable paradigm of complex many-body quantum systems, a two-band Wannier-Stark model, for which diffusion in Hilbert space as well as many-body Landau-Zener processes can be engineered. A cross-over between regular to quantum chaotic spectra is found within the many-body avoided crossings at resonant tunneling conditions. The spectral properties are shown to determine the evolution of states across a cascade of Landau-Zener events. We apply the obtained spectral information to study the non-equilibrium dynamics of our many-body system in different parameter regimes. 
Carlos A. Parra-Murillo, Javier Madro\~nero, Sandro Wimberger
cond-mat.quant-gas nlin.CD quant-ph