3 research outputs found
Processes of Creation and Propagation of Correlations in Large Quantum Particle System
We review new approaches to the description of the evolution of states of large quantum particle systems by means of the marginal correlation operators. Using the definition of marginal correlation operators within the framework of dynamics of correlations governed by the von Neumann hierarchy, we establish that a sequence of such operators is governed by the nonlinear quantum BBGKY hierarchy. The constructed nonperturbative solution of the Cauchy problem to this hierarchy of nonlinear evolution equations describes the processes of the creation and the propagation of correlations in large quantum particle systems. Furthermore, we consider the problem of the rigorous description of collective behavior of quantum many-particle systems by means of a one-particle (marginal) correlation operator that is a solution of the generalized quantum kinetic equation with initial correlations, in particular, correlations characterizing the condensed states of systems
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
On Rigorous Derivation of the Enskog Kinetic Equation
We develop a rigorous formalism for the description of the kinetic evolution
of infinitely many hard spheres. On the basis of the kinetic cluster expansions
of cumulants of groups of operators of finitely many hard spheres the nonlinear
kinetic Enskog equation and its generalizations are justified. It is
established that for initial states which are specified in terms of
one-particle distribution functions the description of the evolution by the
Cauchy problem of the BBGKY hierarchy and by the Cauchy problem of the
generalized Enskog kinetic equation together with a sequence of explicitly
defined functionals of a solution of stated kinetic equation is an equivalent.
For the initial-value problem of the generalized Enskog equation the existence
theorem is proved in the space of integrable functions.Comment: 28 page