Comparison of quantum kinetic theory and time-dependent Dirac equation approaches in vacuum pair production and the bound states resonance enhanced mechanism

A remarkable quantitative agreement is found between the non-Markovian quantum kinetic approach and the time-dependent Dirac equation approach for a large region of Keldysh parameter, in the investigation of electron-positron pair production in the electric fields which is spatially homogeneous and envelope pulse shaped. If a sub-critical bound potential is immersed in this background field, the TDDE results show that the creation probability will be enhanced by the bound states resonance by two orders of magnitude. We also establish a computing resources greatly saved TDDE formalism for spatially homogeneous field.