The aim of this work is the study of a special class of nonequilibrium systems which admits to find exact stationary solutions of the kinetic equations. In particular we investigate canonical-dissipative systems, where the driving terms are determined by the Hamiltonian or other invariants of motion only. We construct systems which drive the system to special invariants of motion and solve the corresponding Fokker-Planck equations. Finally several applications to mean-field problems for fermion and for boson systems are discussed.

We study the bound states of electrons with solitonic excitations in one and two-dimensional atomic systems. We include Morse interactions between the atoms in a temperature range from low to physiological temperatures. The atoms are treated by classical Langevin equations. In a first approach, the places of compressions are visualized by drawing the overlap of the densities of the core electrons. Then we study the effect of nonlinear vibrations on the added, free electrons moving on the background of the atoms. We study the coupled classical and quantum-mechanical dynamics of the electrons on the lattice in tight-binding approximation (TBA). Further we consider the formation of solectrons, i. e., dynamic electron-soliton bound states in adiabatic approximations based on the energy spectrum and the canonical distribution.

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