The effect of frequency chirping on electron-positron pair production in   the one- and two-color laser pulse fields
  The effect of the frequency chirping on momentum spectrum and pair production rate in one- and two-color laser pulse fields is investigated by solving the quantum Vlasov equation. A small frequency chirp shifts the momentum spectrum along the momentum axis. The positive and negative frequency chirp parameters play the same role in increasing the pair number density. The sign change of frequency chirp parameter at the moment $t=0$ leads pulse shape and momentum spectrum to be symmetric, and the number density to be increased. The number density of produced pairs in the two-color pulse field is much higher than that in the one-color pulse field and the larger frequency chirp pulse field dominates more strongly. In the two-color pulse fields, the relation between the frequency ratio of two colors and the number density is not sensitive to the parameters of small frequency chirp added in either low frequency strong field or high frequency weak field but sensitive to the parameters of large frequency chirp added in high frequency weak field. 
Nuriman Abdukerim, Zi-Liang Li and Bai-Song Xie
quant-ph hep-ph