Massless quark production in chromoelectric field with back reaction

We study the massless quark production in $SU(2)$ gauge chromoelectric field by single-time Wigner function covariantly with back reaction. The evolution of field and current are investigated. For a phenomenological distribution function, both the time and momentum dependence have been studied. Interesting phenomena are found, which are: when considering the back reaction, the yield of quark production is higher than the Bjorken expanding field, and momentum 'gap' with confinement phenomenon exists in the phenomenological distribution function. To have a better understanding on the phenomena, components of the Wigner function are qualitatively analyzed.