Given the recent interest in the non-equilibrium quenching dynamics
of quantum many-body systems across quantum critical points (QCPs),
the studies involving quenching dynamics of a topological system
across a QCP have emerged as a rapidly growing field of research.
Especially, the quenching dynamics of a topological insulator and
the p-wave superconductors have been explored in this connection.
In this talk, I will discuss the dynamics of a Majorana edge mode
in a p-wave superconducting chain following sudden and slow changes
of a parameter of the Hamiltonian across QCPs. The survival probability
of an edge Majorana as a function of time is studied when
the system is suddenly driven from one topological phase to the other
and also to the QCPs separating these phases. In the context
of slow quenching dynamics of a finite p-wave superconducting chain
with a complex hopping term, we ask the question whether an edge
Majorana can be transported from one topological phase to the other
across a gapless region.