Time-dependent Ginzburg-Landau equation and Boltzmann transport equation   for charge-density-wave conductors
  The time-dependent Ginzburg-Landau equation and the Boltzmann transport equation for one-dimensional charge-density-wave (CDW) conductors are derived from a microscopic model by applying the Keldysh Green's function approach under a quasiclassical approximation. The effects of external electric field and impurity pinning of the CDW are fully taken into account without relying on a phenomenological argument. These equations simultaneously describe spatiotemporal dynamics of both the CDW and quasiparticles, so they serve as a powerful tool to analyze various nonequilibrium phenomena, such as the current conversion between the CDW condensate and quasiparticles mediated by phase slips. It is shown that, in typical situations, the equations correctly describe the nonlinear behavior of electric conductivity in a simpler manner. 
Yositake Takane, Masahiko Hayashi, and Hiromichi Ebisawa
cond-mat.str-el