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Comparison of semiclassical and Wigner function methods in pair production in rotating fields

We present a comparison of two methods to compute the momentum spectrum and the Schwinger pair creation rate for pulsed rotating electric fields: one based upon the real-time Dirac--Heisenberg--Wigner (DHW) formalism and a semiclassical approximation based on a scattering ansatz. For the semiclassical method we propose to either perform numerical calculations or an additional approximation based on an analytical solution for the constant rotating field. We find that both numerical methods are complementary with respect to computation time as well as accuracy. The approximate method shows the same qualitative features while being computationally much faster. We additionally find that the unequal production of pairs in different spin states reported for constant rotating fields with the scattering method is in agreement with the Wigner function method.