Evolution of correlation operators of large particle quantum systems. (English) Zbl 1389.82001

The author develops an approach to describe an evolution of states of quantum systems of large number of particles by means of marginal correlation operators. A non-perturbative solution of the Cauchy problem for the hierarchy of nonlinear equations for marginal correlation operators is constructed. For the case where the initial states are determined by a one-particle density operator, the mean field asymptotic behavior of solutions is established.


82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
82C21 Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics
35Q40 PDEs in connection with quantum mechanics
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