DERIVATION OF A KINETIC-EQUATION FOR AN INHOMOGENEOUS GAS OF PARTICLES BEARING A SPIN AND OBEYING QUANTUM STATISTICS

The kinetic equation for an inhomogeneous dilute gas of particles bearing a spin and obeying quantum statistics is derived from a general method based on correlation patterns. This equation takes into account the delocalization of the collision process and we consider the case where spin polarization of the gas is present. The equation obtained for the one-body Wigner density and spin polarization function can be used for the computation of transport coefficients of the gas since we show that it leads to the local conservation laws for the matter density, spin polarization density, momentum and energy, including potential energy contributions. The two-body Wigner distribution function is displayed as a functional, generated by the dynamics, of the one-body distribution without resourse to any molecular chaos hypothesis. © 1990.