  It has been well established that the origin of p-wave superconductivity is
the balance between pair creation and annihilation, described by the spin-less
fermionic Kitaev model. In this work, we study the dynamics of a composite
system where the pair source and drain are spatially separated by a long
distance. We show that this non-Hermitian system possesses a high-order
exceptional point (EP) when only a source or drain is considered. The EP
dynamics provide a clear picture: A pair source can fully fill the system with
pairs, while a drain can completely empty the system. When the two coexist
simultaneously, the dynamics depend on the distance and the relative phase
between the pair creation and annihilation terms. Analytical analysis and
numerical simulation results show that the superconducting state can be
dynamically established at the resonant pair source and drain: from an initial
empty state to a stationary state with the maximal pair order parameter. It
provides an alternative way of understanding the mechanism of the
nonequilibrium superconducting state.
