Soft Modes, Quantum Transport and Kinetic Entropy

The effects of the propagation of particles which have a finite life-time and an according width in their mass spectrum are discussed in the context of transport descriptions. In the first part the coupling of soft photon modes to a source of charged particles is studied in a classical model which can be solved completely in analytical terms. The solution corresponds to a re-summation of certain field theory diagrams. The general properties of broad resonances in dense finite temperature systems are discussed at the example of the $\rho$-meson in hadronic matter. The second part addresses the problem of transport descriptions which also account for the damping width of the particles. The Kadanoff--Baym equation after gradient approximation together with the $\Phi$-derivable method of Baym provides a self-consistent and conserving scheme. Memory effects appearing in collision term diagrams of higher order are discussed. We derive a generalized expression for the nonequilibrium kinetic entropy flow, which includes corrections from fluctuations and mass-width effects. In special cases an $H$-theorem is proved. Memory effects in collision terms provide contributions to the kinetic entropy flow that in the Fermi-liquid case recover the famous bosonic type $T^3 \ln T$ correction to the specific heat of liquid Helium-3.