Sudden jumps and plateaus in the quench dynamics of a Bloch state

ake a one-dimensional tight binding chain and put a particle in some Bloch state, then quench it by suddenly changing the potential of some site. In its time evolution, the probability density of the wave function at an arbitrary site constantly jumps between plateaus. This phenomenon in the real space complements the previous finding in the momentum space (Zhang and Yang, arXiv:1601.03569) that the survival probability of the particle in the initial Bloch state shows cusps periodically. Thus emerges a comprehensive picture of the time evolution of the quenched Bloch state. Underlying the cusps and jumps is the exactly solvable, nonanalytic dynamics of a fictitious model.