Extracting information from non adiabatic dynamics: excited symmetric   states of the Bose-Hubbard model
  Using Fourier transform on a time series generated by unitary evolution, we extract many-body eigenstates of the Bose-Hubbard model corresponding to low energy excitations, which are generated when the insulator-superfluid phase transition is realized in a typical experiment. The analysis is conducted in a symmetric external potential both without and with and disorder. A simple classification of excitations in the absence disorder is provided. The evolution is performed assuming the presence of the parity symmetry in the system rendering many-body quantum states either symmetric or antisymmetric. Using symmetry-breaking technique, those states are decomposed into elementary one-particle processes. 
M. Lacki, D. Delande, and J. Zakrzewski
cond-mat.quant-gas quant-ph