  We identify persistent oscillations in a nonintegrable quantum Ising chain
left behind by a rapid transition into a ferromagnetic phase. In the integrable
chain with nearest-neighbor (NN) interactions, the nature, origin, and decay of
post-transition oscillations are tied to the Kibble-Zurek mechanism (KZM).
However, when coupling to the next nearest neighbor (NNN) is added, the
resulting nonintegrable Ising chain (still in the quantum Ising chain
universality class) supports persistent post-transition oscillation: KZM-like
oscillations turn into persistent oscillations of transverse magnetization.
Their longevity in our simulations is likely limited only by the numerical
accuracy. Their period differs from the decaying KZM oscillation but their
amplitude depends on quench rate. Moreover, they can be excited by driving in
resonance with the excitations' energy gap. Thus, while one might have expected
that the integrability-breaking NNN coupling would facilitate relaxation, the
oscillations we identify are persistent. At low to medium transverse fields,
they are associated with Cooper pairs of Bogoliubov quasiparticles -- kinks.
This oscillation of the pair condensate is a manifestation of quantum
coherence.
