In this paper we consider the 1D Schrödinger operator H with periodic point interactions. We show an L1 − L∞ bound for the time evolution operator e−itH restricted to each energy band with decay order O(t−1/3) as t → ∞, which comes from some kind of resonant state. The order O(t−1/3) is optimal for our model. We also give an asymptotic bound for the coefficient in the high energy limit. For the...
