In this work,the three-period quantum walk model on one-dimensional infinite lattice line is extended to include two asymmetric phase-accumulating operators.The energy band structure and the winding number,which characters the topological properties of the system,are calculated.The winding number is represented by the phase accumulation in the process of quantum walk.Furthermore,we introduce the time-dependent phase and investigate the dynamics of three-period quantum walk.It is found that the probability distribution behaves Bloch oscillation as that an electron subjected to a constant electric field in a one-dimension-al lattice.In particular,the topological winding number of three-period quantum walk is equal to the number of turning points over a period of Bloch oscillation.As a conclusion,the topological properties of the system can be viewed from the point of system dynami-cal evolution.
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