Edge mode dynamics in long-range Kitaev model

In this paper we study the dynamics of long-range pairing and hopping p-wave superconducting chain after a ‎sudden quench of chemical potential. We have shown that the quantum-classical phase transition occurs ‎when the system is quenched to the critical point and the Loschmidt echo shows perfect periodic oscillations. ‎Moreover we have studied the dynamical phase transition for a quench across the critical point. Our analysis ‎shows that the dynamical phase transition occurs for the cases where the system initially prepared in the ‎massless edge modes. While the system does not show dynamical phase transition when the system is ‎prepared in the massive edge modes, even the quench crossing the critical point‎‎.