|Kinks and cusps in the transition dynamics of a Bloch state|
We discuss the transition dynamics of a Bloch state in a 1D tight binding chain, under two scenarios, namely, weak periodical driving  and sudden quench . In the former case, the survival probability of the initial Bloch state shows kinks periodically; it is a piece-wise linear function of time. In the latter, the survival probability (Loschmidt echo in this case) shows cusps periodically; it is a piece-wise quadratic function of time. Kinks in the former case are a perturbative effect, while cusps in the latter are a non-perturbative effect. Relevant stories and links to quantum optics models and the transerse field Ising model will be mentioned.
 J. M. Zhang and M. Haque, arXiv:1404.4280.
 J. M. Zhang and H. T. Yang, arXiv:1601.03569