Nonadiabatic quantum Vlasov equation in spinor QED

The nonadiabatic quantum Vlasov equation in spinor QED is derived, and its relation to the well-known adiabatic one is established by three different methods. One is by deriving an explicit analytical expression. The second is by utilizing the Dirac equation in the length gauge, and the last is by introducing a weak and slowly varying counterfield. The relations obtained using the first two methods are instantaneous. Moreover, a comparative analysis of the nonadiabatic quantum Vlasov equations in both spinor and scalar QED is performed by investigating the time evolution of the distribution functions for a given momentum and the asymptotic momentum distributions of particles created by an electric field with and without an additional counterfield. It is found that after the external field is turned off, the oscillation periods of the distribution functions in both spinor and scalar QED equal pi divided by the positive eigenvalue of the Hamiltonian. The asymptotic momentum distributions in spinor and scalar QED show a novel out-of-phase behavior that cannot be explained by the conventional Stokes phenomenon. These results will further deepen our understanding of quantum Vlasov equations and their applications in vacuum pair production. Published by the American Physical Society 2024