A nonperturbative solution of the nonlinear BBGKY hierarchy for marginal correlation operators

Gerasimenko, V. I.; Polishchuk, Dmytro

doi:10.1002/mma.2753

Cited by 8 publications

(32 citation statements)

References 24 publications

(116 reference statements)

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“…Thus, in case of initial states specified by one-particle (marginal) density operator (23) we establish that the dual quantum Vlasov hierarchy (19) for additive-type marginal observables describes the evolution of a quantum large particle system just as the non-Markovian quantum Vlasov-type kinetic equation with initial correlations (26).…”

Section: The Quantum Vlasov-type Kinetic Equation With Initial Correlmentioning

confidence: 80%

“…It should be noted that equations set (19) has the structure of recurrence evolution equations. We give several examples of the evolution equations of the dual quantum Vlasov hierarchy (19) in terms of operator kernels of the limit marginal observables…”

Section: ) Of Limit Marginal Observables (17) Is a Generalized Glomentioning

confidence: 99%

“…Thus, for arbitrary initial states in the mean field scaling limit the kinetic evolution of quantum many-particle systems is described in terms of limit marginal observables (17) governed by the dual quantum Vlasov hierarchy (19).…”

Section: (22)mentioning

confidence: 99%

“…We note that the general approach to the description of the evolution of states of quantum many-particle systems within the framework of correlation operators and marginal correlation operators was given in paper [19].…”

Section: The Propagation Of Initial Correlations In a Mean Field Limitmentioning

confidence: 99%

“…Thus, in case of the limit k-ary marginal observables solution (22) of the dual quantum Vlasov hierarchy (19) is equivalent to a property of the propagation of initial correlations for the k-particle marginal density operator in the sense of equality (28) or in other words the mean field scaling dynamics does not create correlations.…”

Section: The Propagation Of Initial Correlations In a Mean Field Limitmentioning

confidence: 99%

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New approach to derivation of quantum kinetic equations with initial correlations

Gerasimenko

2015

Carpathian Math. Publ.

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We propose a new approach to the derivation of kinetic equations from dynamics of large particle quantum systems, involving correlations of particle states at initial time. The developed approach is based on the description of the evolution within the framework of marginal observables in scaling limits. As a result the quantum Vlasov-type kinetic equation with initial correlations is constructed and the statement relating to the property of a propagation of initial correlations is proved in a mean field limit.

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Section: The Quantum Vlasov-type Kinetic Equation With Initial Correlmentioning

confidence: 80%

Section: ) Of Limit Marginal Observables (17) Is a Generalized Glomentioning

confidence: 99%

Section: (22)mentioning

confidence: 99%

Section: The Propagation Of Initial Correlations In a Mean Field Limitmentioning

confidence: 99%

Section: The Propagation Of Initial Correlations In a Mean Field Limitmentioning

confidence: 99%

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New approach to derivation of quantum kinetic equations with initial correlations

Gerasimenko

2015

Carpathian Math. Publ.

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On Semigroups of Large Particle Systems and Their Scaling Asymptotic Behavior

Gerasimenko

Fedchun

2014

Springer Proceedings in Mathematics &Amp; Statistics

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Abstract. 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 (semiinvariants) 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.

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Processes of creation and propagation of correlations in quantum many-particle systems

Gerasimenko¹

2016

Dopov. Nac. akad. nauk Ukr.

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A nonperturbative solution of the nonlinear BBGKY hierarchy for marginal correlation operators

Cited by 8 publications

References 24 publications

New approach to derivation of quantum kinetic equations with initial correlations

New approach to derivation of quantum kinetic equations with initial correlations

On Semigroups of Large Particle Systems and Their Scaling Asymptotic Behavior

Processes of creation and propagation of correlations in quantum many-particle systems

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