Mean Field Asymptotic Behavior of Quantum Particles with Initial Correlations

In the paper we consider the problem of the rigorous description of the kinetic evolution in the presence of initial correlations of quantum large particle systems. One of the developed approaches consists in the description of the evolution of quantum many-particle systems within the framework of marginal observables in mean field scaling limit. Another method based on the possibility to describe the evolution of states within the framework of a one-particle marginal density operator governed by the generalized quantum kinetic equation in case of initial states specified by a one-particle marginal density operator and correlation operators.Comment: 17 page

On the Initial-Value Problem to the Quantum Dual BBGKY Hierarchy

We develop a rigorous formalism for the description of the evolution of observables in quantum systems of particles. We construct a solution of the initial-value problem to the quantum dual BBGKY hierarchy of equations as an expansion over particle clusters whose evolution are governed by the corresponding-order dual cumulant (dual semi-invariant) of the evolution operators of finitely many particles. For initial data from the space of sequences of bounded operators the existence and uniqueness theorem is proved.Comment: 22 page

On Semigroups of Large Particle Systems and their Scaling Asymptotic Behavior

We consider semigroups of operators for hierarchies of evolution equations of large particle systems, namely, of the dual BBGKY hierarchy for marginal observables and the BBGKY hierarchy for marginal distribution functions. We establish that the generating operators of the expansions for one-parametric families of operators of these hierarchies are the corresponding order cumulants (semi-invariants) of semigroups for the Liouville equations. We also apply constructed semigroups to the description of the kinetic evolution of interacting stochastic Markovian processes, modeling the microscopic evolution of soft active matter. For this purpose we consider the mean field asymptotic behavior of the semigroup generated by the dual BBGKY hierarchy for marginal observables. The constructed scaling limit is governed by the set of recurrence evolution equations, namely, by the Vlasov-type dual hierarchy. Moreover, the relationships of this hierarchy of evolution equations with the Vlasov-type kinetic equation with initial correlations are established.Comment: 17 pages. arXiv admin note: text overlap with arXiv:1308.450

Quantum Kinetic Evolution of Marginal Observables

We develop a rigorous formalism for the description of the evolution of observables of quantum systems of particles in the mean-field scaling limit. The corresponding asymptotics of a solution of the initial-value problem of the dual quantum BBGKY hierarchy is constructed. Moreover, links of the evolution of marginal observables and the evolution of quantum states described in terms of a one-particle marginal density operator are established. Such approach gives the alternative description of the kinetic evolution of quantum many-particle systems to generally accepted approach on basis of kinetic equations.Comment: 18 page

Quantitative estimation of business activity in the market of tourist services

The critical analysis of approaches of various authors to definition of the basic quantity indicators of the market of tourist services is carried out. Methods of calculation of such important characteristics of the tourist markets are offered, such as: capacity of the real and potential markets, the size of the market, market structure, factor of a saturation of the market. Information sources for an exact establishment of size of the specified are considered