Mean Field Asymptotic Behavior of Quantum Particles with Initial Correlations

@inproceedings{Gerasimenko2014MeanFA,
  title={Mean Field Asymptotic Behavior of Quantum Particles with Initial Correlations},
  author={Viktor Ivanovich Gerasimenko},
  year={2014}
}
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… 
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Processes of Creation and Propagation of Correlations in Large Quantum Particle System

  • V. Gerasimenko
  • Mathematics, Physics
    Panorama of Contemporary Quantum Mechanics - Concepts and Applications
  • 2019
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…

On Operators Generated by Density Matrix

In this survey the possible approaches to the description of the evolution of states of quantum many-particle systems by means of the possible modifications of the density operator which kernel known…

References

SHOWING 1-10 OF 32 REFERENCES

Heisenberg picture of quantum kinetic evolution in mean-field limit

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…

Evolution of correlations of quantum many-particle systems

We consider the origin of the microscopic description of correlations in quantum systems. For correlation operators that give the alternative description of the quantum state evolution of…

A description of the evolution of quantum states by means of the kinetic equation

We develop a rigorous formalism for describing the evolution of states of quantum many-particle systems in terms of a one-particle density operator. For initial states which are specified in terms of…

On quantum kinetic equations of many-particle systems in condensed states

Mean Field Asymptotics of Generalized Quantum Kinetic Equation

Dynamics of correlations of Bose and Fermi particles

We discuss the origin of the microscopic description of correlations in quantum many‐particle systems obeying Fermi–Dirac and Bose–Einstein statistics. For correlation operators that give the…

Quantum Dynamics with Mean Field Interactions: a New Approach

We propose a new approach for the study of the time evolution of a factorized N-particle bosonic wave function with respect to a mean-field dynamics with a bounded interaction potential. The new…

Mean-Field Limit and Semiclassical Expansion of a Quantum Particle System

Abstract.We consider a quantum system constituted by N identical particles interacting by means of a mean-field Hamiltonian. It is well known that, in the limit N → ∞, the one-particle state obeys to…

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…

On the Dynamics of Large Particle Systems in the Mean Field Limit

This course explains how the usual mean field evolution partial differential equations (PDEs) in Statistical Physics—such as the Vlasov-Poisson system, the vorticity formulation of the…