Transport equations for dilute gases with internal degrees of freedom

Abstract

A quantum-theoretical transport equation for dilute gases with internal degrees of freedom, due to Waldmann and Snider, is generalized to the case of arbitrary level spacing between the internal energy levels. It turns out that the diagonal matrix elements in the internal energy of the singlet density operator, ϱ (1), no longer obey a closed equation. For sufficient level spacing the Waldmann-Snider equation follows as a limiting case, provided ϱ (1) is diagonal in the internal energy at the initial time. If this is not so a more complicated equation holds which, after linearization, reduces to a set of decoupled equations for diagonal and off-diagonal matrix elements of ϱ (1) in the internal energy, the equation for the diagonal part being the linearized Waldmann-Snider equation. The case that a homogeneous constant external field is present has been treated as well.