We advance a new analytical method for the Dirac equation in two-dimensional, homogeneous, time-dependent electric fields, which expresses the Cauchy problem of the two-component spinor and its derivative as the time-ordered integral of the transition rate of the time-dependent eigenspinors and the time-dependent energy eigenvalues. The in-vacuum at later times evolves from that at the past infinity and continuously make transitions between eigenspinors and between positive and negative frequencies of the time-dependent energy eigenvalues. The production of electron and positron pairs is given by the coefficient of the negative frequency at the future infinity which evolves from the positive frequency at the past infinity. In the adiabatic case when the time scale for the rotation of eigenspinors and energy eigenvalues is much longer than the electron Compton time, we find the spin-resonance effect on the pair production, which is simply determined by the spin rotation, the pair production and the continuous transmission coefficients between the energy eigenvalues without the change of spin states.
Novel five-dimensional rotating Lifshitz black holes with electric and axionic charges
Universidad Católica del Maule（马乌莱天主教大学）；Universidad Nacional Autónoma de Honduras（洪都拉斯国立自治大学）；Benemérita Universidad Autónoma de Puebla（普埃布拉自治美利坚大学）；Universidad de Concepción（康塞普西翁大学）；South China University of Technology（华南理工大学）
Interaction of the magnetic quadrupole moment of a non-relativistic particle with an electric field in the background of screw dislocations with a rotating frame
