Fluctuations in non-equilibrium electron gas: Effect of quantum statistics

Here we develop a mathematical apparatus to describe quasi-classical fluctuations in a non-equilibrium electron gas with electron-electron collisions. We substantiate the method by deriving, from general principles of quantum kinetics, an equation recently proposed by us for an equal-time electron-electron correlation function. The derivation is performed using the kinetic diagram technique. In degenerate non-equilibrium gas, the theory predicts that there exists a specific equal-time correlation between electrons. Due to the prevalence of small-angle electron-electron scattering, the equation in question takes a rather simple and treatable form (the Coulomb-type electron-electron interaction stands out against the background of all other types of interaction as one that does not generate, in the framework of quasi-classical approach, any direct exchange effects).