Failure of the Weak-Coupling Model in the Transport Theory of Dense Real Gases

It is shown that the weak-coupling limit is not valid for the third-order term in the density expansion of quantum or classical transport coefficients. The weak-coupling limit is not valid in the sense that it does not preserve the qualitative features of real gases and, hence, is useless within the context of the transport divergence problem. In fact, it is shown that, although the weak-coupling limit of the recollision part of the quantum four-particle collision operator diverges, its contribution to transport coefficients actually converges (whereas this contribution is known to diverge logarithmically when no weak-coupling limit is taken). A rather curious behavior is uncovered for the quantum weak-coupling limit of the recollision part of the four-particle collision operator. It is found that the matrix elements of this operator grow as $t^{\frac{1}{2}}$ and oscillate rapidly. This growth, which is faster than logarithmic in $t$, is associated with a spatial overlapping of broadening wave packets. Because of the accompanying oscillation, however, it does not present any divergence problem to transport theory.