Excited-state quantum phase transitions and periodic dynamics
  We investigate signatures of the excited-state quantum phase transition in the periodic dynamics of the Lipkin-Meshkov-Glick model and the Tavis-Cummings model. In the thermodynamic limit, expectation values of observables in eigenstates of the system can be calculated using classical trajectories. Motivated by this, we suggest a method based on the time evolution of the finite-size system, to find singularities in observables, which arise due to the excited-state quantum phase transition. 
G. Engelhardt, V. M. Bastidas, W. Kopylov and T. Brandes
cond-mat.quant-gas quant-ph