Collisional Transfer Contributions in the Quantum Theory of Transport Coefficients

The quantum-mechanical BBGKY equations are solved in terms of the phase-space transformation functions. Introducing the molecular-chaos assumption, the pair distribution function is obtained. In the binary-collision approximation, this leads to a generalized Boltzmann equation, in which the collisional-transfer contributions are included. This equation is solved by the method of Chapman and Enskog, and expressions for the transport coefficients are obtained, which are given entirely in terms of the solutions of the two-particle Schrödinger equation. The classical limit (ℏ→0) of the expressions are also derived. The heat flux is found to contain contributions which are proportional to the gradient in density. The significance of these terms, which are of the order ℏ4, is discussed.