Overcritical PTPT-symmetric square well potential in the Dirac equation

We study scattering properties of a PTPT-symmetric square well potential with real depth larger than the threshold of particle–antiparticle pair production as the time component of a vector potential in the Dirac equation. Spontaneous pair production inside the well becomes tiny beyond the strength at which discrete bound states with real energies disappear, consistently with a spontaneous breakdown of PTPT symmetry.