KINETIC-EQUATIONS FOR A NONIDEAL QUANTUM SYSTEM

In the framework of real-time Green's functions, the general kinetic e quations are investigated in a first-order gradient expansion. Within this approximation, the problem of the reconstruction of the two-time correlation functions from the one-time Wigner function was solved. Fo r the Wigner function, a cluster expansion is found in terms of a quas iparticle distribution function. In equilibrium, this expansion leads to the well-known generalized Beth-Uhlenbeck expression of the second virial coefficient. As a special case, the T-matrix approximation for the self-energy is investigated. The quantum kinetic equation derived thus has, besides the (Markovian) Boltzmann collision integral, additi onal terms due to the retardation expansion which reflect memory effec ts. Special interest is paid to the case that bound states exist in th e system. It is shown that the bound state contribution, which can be introduced via a bilinear expansion of the two-particle T matrix, foll ows from the first-order retardation term in the general kinetic equat ion. The full Wigner function is now a sum of one function describing the unbound particles and another one for the bound state contribution . The latter two functions have to be determined from a coupled set of kinetic equations. In contrast to the quantum Boltzmann equation, ene rgy and density of a nonideal system are conserved.