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Quantum fluctuations and rate of convergence towards mean field dynamics. (English) Zbl 1186.82051

The authors consider a system of \(N\)-boson described by a mean field Hamiltonian, with a coupling constant \(1/N\) in front of the two-body interaction potential terms. In the limit of large \(N\) an initially factorized state can be approximated by a factorized state, whose one-particle wave function obeys the nonlinear Hartree equation. This approximation is to be understood in terms of convergence of marginal densities. The authors address this problem using a different technique with respect to the study of the BBGKY hierarchy, and obtain improved bounds on the difference between the one-particle density associated with the solution of the \(N\)-body Schrödinger equation and the one-particle wavefunction solution of the Hartree equation.

MSC:

82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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