Non-Markovian Boltzmann equation

A quantum kinetic equation for strongly interacting particles (generalized binary collision approximation, ladder or T-matrix approximation) is derived in the framework of the density operator technique. In contrast to conventional kinetic theory, which is valid on time scales large as compared to the collision (correlation) time only, our approach retains the full time dependencies, especially also on short time scales. This means, retardation and memory eeects resulting from the dynamics of binary correlations, and initial correlations are included. Furthermore, the resulting kinetic equation conserves total energy (the sum of kinetic and potential energy). The second aspect of generalization is the inclusion of many-body eeects, such as selfenergy, i.e. renormalization of single-particle energies and damping. To this end, we introduce an improved closure relation to the BBGKY (Bogolyubov-Born-Green-Kirkwood-Yvon) hierarchy. Furthermore, in order to express the collision integrals in terms of familiar scattering quantities (MMller operator, T-matrix), we generalize the methods of quantum scattering theory by inclusion of medium eeects. 1 To illustrate the eeects of memory and damping, results of numerical simulations are presented. manuscript with 51 pages and 4 gures (4 additional pages),