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The Anderson localization phase transition in the Aubry-Andr\'e-Harper (AAH)model with \textit{p}-wave superconducting (SC) pairing is numericallyinvestigated by suddenly changing the on-site potential from zero to variousfinite values which fall into the extended, critical and localized phaseregimes shown in this model. The time evolutions of entanglement entropy (EE),mean width of wave packets and Loschmidt echo of the system exhibit distinctbut consistent dynamical signatures in those three phases. Specifically, the EEgrows as a power function of time with the exponent of which varies in theextended phase but keeps almost unchanged in the critical phase for differentquench parameters. However, if the system is in the localized phase after aquench, the EE grows much slower and will soon get saturated. Thetime-dependent width of wave packets in the system shows similar behaviors asthe EE. In addition, from the perspective of dynamical phase transition, wefind that the Loschmidt echo oscillates and always keeps finite when the systemis quenched in the extended phase. In contrast, in the critical or localizedphase, the echo will reach to zero at some time intervals or will decay almostto zero after a long-time evolution. The universal features of these quantitiesin the critical phase of the system with various SC pairing amplitudes are alsoobserved.

Quench dynamics in the Aubry-Andr\'e-Harper model with \textit{p}-wave superconductivity