Mean field propagation of Wigner measures and BBGKY hierarchies for general bosonic states

Abstract

Contrary to the finite dimensional case, Weyl and Wick quantizations are no more asymptotically equivalent in the infinite dimensional bosonic second quantization. Moreover neither the Weyl calculus defined for cylindrical symbols nor the Wick calculus defined for polynomials are preserved by the action of a nonlinear flow. Nevertheless taking advantage carefully of the information brought by these two calculuses in the mean field asymptotics, the propagation of Wigner measures for general states can be proved, extending to the infinite dimensional case a standard result of semiclassical analysis.

arXiv comment39 pages

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Cited by in corpus (4)

• On the rate of convergence for the mean field approximation of many-body quantum dynamics
• On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti
• Magnetic Schrödinger Operators as the Quasi-Classical Limit of Pauli-Fierz-type Models
• Quantum mean field asymptotics and multiscale analysis