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. The kinks and cusps are reminiscent of the so-called dynamical phase transtion termed by Heyl et al. .
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