Fidelity of an electron in one-dimensional determined potentials

We numerically study the fidelity of an electron in the one-dimensional Harper model and in the one-dimensional slowly varying potential model. Our results show that many properties of the two models can be well reflected by the fidelity: (i) the mobility edge and metal--insulator transition can be characterized by the static fidelity; (ii) the extended state and localized state can be identified by the dynamic fidelity. Therefore, it may broaden the applied areas of the fidelity.