We compare the creation rates for particle-antiparticle pairs produced by a supercritical force field for fermionic and bosonic model systems. The rates obtained from the Dirac and Klein-Gordon equations can be computed directly from the quantum-mechanical transmission coefficients describing the scattering of an incoming particle with the supercritical potential barrier. We provide a unified framework that shows that the bosonic rates can exceed the fermionic ones, as one could expect from the Pauli-exclusion principle for the fermion system. This imbalance for small but supercritical forces is associated with the occurrence of negative bosonic transmission coefficients of arbitrary size for the Klein-Gordon system, while the Dirac coefficient is positive and bound by unity. We confirm the transmission coefficients with time-dependent scattering simulations. For large forces, however, the fermionic and bosonic pair-creation rates are surprisingly close to each other. The predicted pair creation rates also match the slopes of the time-dependent particle probabilities obtained from large-scale ab initio numerical simulations based on quantum field theory.
Cheng, T; Ware, M R.; Su, Q; and Grobe, Rainer, "Pair creation rates for one-dimensional fermionic and bosonic vacua" (2009). Faculty publications – Physics. Paper 21.