Derivation Of non-Markovian Kinetic Equations Research Articles

Inertial mechanism: Dynamical mass as a source of particle creation

A kinetic theory of vacuum particle creation under the action of an inertial mechanism is constructed within a nonperturbative dynamical approach. At the semi-phenomenological level, the inertial mechanism corresponds to quantum field theory with a time-dependent mass. At the microscopic level, such a dependence may be caused for different reasons: the non-stationary Higgs mechanism, the influence of a mean field or condensate, the presence of a conformal multiplier in the scalar-tensor gravitation theory, etc. In what follows, a kinetic theory in the collisionless approximation is developed for scalar, spinor, and massive vector fields in the framework of the oscillator representation, which is an effective tool for transition to the quasiparticle description and for derivation of non-Markovian kinetic equations. Properties of these equations and relevant observables (particle number and energy densities, pressure) are studied. The developed theory is applied here to describe the vacuum matter creation in conformal cosmological models and explain the observed number density of photons in the cosmic microwave background radiation. As another example, the self-consistent evolution of scalar fields with non-monotonic self-interaction potentials (the W-potential and Witten-Di Vecchia-Veneziano model) is considered. In particular, conditions for the appearance of tachyonic modes and the problem of the relevant definition of a vacuum state are discussed.

Consistent account of force correlations in a many-particle derivation of non-Markovian kinetic equations for chemical reactions in solutions

The previously proposed many-particle method for the derivation of kinetic equations of chemical reactions in liquid solutions is applied to the consideration of irreversible reaction A + B → C + B . Both force and chemical space correlations resulting from the force interactions between all reactants and chemical reaction between A and B species are taken into account on the same basis. Examination of chemical and force interactions in the system of reactants shows that their contributions to the time evolution of correlation patterns differ essentially because of different analytical properties of the above interactions. It is shown that proper account of the force interaction between reactants corresponds to the change in the character of a relative mobility in the ultimate evolution of a reaction pair (ultimate propagator), not only in the process of correlation accumulation in effective pairs, as is sometimes assumed.

A many-particle derivation of non-Markovian kinetic equations of reversible reaction A+ B⇌ C in solutions based on the effective pairs approach

The non-Markovian kinetic equations for local concentrations have been derived in the effective pairs approximation on the basis of the hierarchy for correlation patterns of the reversible reaction A+ B⇌ C. The equations are shown to agree with the kinetic and thermodynamic detailed balancing principles. As compared to the integral encounter theory equations obtained earlier, the above equations have a wider time range of applicability, and may form the basis for the development of a binary approximation for the reversible reaction A+ B⇌ C in solutions.

A scaling procedure in a many-particle derivation of the non-Markovian binary kinetic equations of the reaction A+ B→ B in liquid solutions

A mathematically rigorous scaling procedure for the derivation of binary non-Markovian kinetic equations has been developed. Though the procedure refers to the irreversible reaction A+ B→ B, it can serve as a reliable basis for selecting diagrams in regular many-particle derivation of non-Markovian kinetic equations for other types of elementary chemical reactions in liquid solutions.

The Landau equation including memory and energy conservation

In the context of the reduced density operator technique the derivation of non-Markovian kinetic equations is briefly reviewed. It is shown that the time retardation in the collision integrals leads to total energy conservation, while the ordinary quantum Boltzmann equation provides only kinetic energy conservation.