  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.
