Die Boltzmanngleichung und mögliche Wege zur Entwicklung dynamischer Methoden in der kinetischen Theorie

Nonlinear relaxation in nonequilibrium oscillators: Bose–Einstein-like condensation in a dissipative structure

“…However, for this particular problem, symmetry properties make null several terms, and those surviving in Eq. (12) are those that correspond: (a)To an equivalent of the Golden Rule of quantum mechanics averaged over the nonequilibrium ensemble ± they are terms with coecients s À1 , M 1 and M 2 , but it must be noticed that the two with M 1 vanish because they correspond to processes that are not allowed because energy conservation in the scattering event is not possible (we recall that the frequency of the phonons of the bath is lower than that of the vibrations under consideration), and M 2 gives a negligible contribution in this case of a very narrow frequency-dispersion relation x q ; (b) To terms, those with coecient K, that are the fourth-order contribution in Born's perturbation series averaged over the nonequilibrium ensemble.…”

“…(12), for the population of the k-mode is composed of several contributions: The ®rst is the one associated to the pumping eects (from the external source) which leads the system further and further away from equilibrium as I (the intensity of the source) is increased. The second contribution accounts for relaxation of the population in excess of equilibrium, created by the source, to the thermal bath thus diminishing the value of the population.…”

A Consistent Description of Kinetics and Hydrodynamics of Systems of Interacting Particles by Means of the Nonequilibrium Statistical Operator Method

“…It does mean that an abbreviated description of nonequilibrium states is available, and the total nonequilibrium distribution function depends on time via f 1 (x; t). In such a case, the quasiequilibrium distribution function ̺ q x N ; t reads [52,53]: 8) where e is the natural logarithm base. Then, the Liouville equation with a small source (2.7) in view of (2.8) corresponds to the abbreviated description of time evolution of the system on a kinetic stage, when only a one-particle distribution function is considered as a slow variable.…”

“…As it is known [51,53], the quasiequilibrium distribution function (2.23) corresponds to the Boltzmann entropy of a dilute gas:…”

Quantum Kinetic Equations: Correlation Dynamics and Selfenergy

“…Substantial contributions are dm due to B&winkel [7] and Zubarev [9]. Explicit non-Mmkovian collision integrals were derived by Silin [4] and by netictpotential) energy of the system.…”