Mean field limit for bosons with compact kernels interactions by Wigner measures transportation. (English) Zbl 1302.82075
Summary: We consider a class of many-body Hamiltonians composed of a free (kinetic) part and a multi-particle (potential) interaction with a compactness assumption on the latter part. We investigate the mean field limit of such quantum systems following the Wigner measures approach. We prove in particular the propagation of these measures along the flow of a nonlinear Hartree field equation. This enhances and complements some previous results of the same type shown by Z. Ammari and F. Nier [ibid. 50, No. 4, 042107, 16 p. (2009; Zbl 1214.81089); J. Math. Pures Appl. (9) 95, No. 6, 585-626 (2011; Zbl 1251.81062)], and J. Fröhlich et al. [Commun. Math. Phys. 271, No. 3, 681-697 (2007; Zbl 1172.82011)].{
©2014 American Institute of Physics}
©2014 American Institute of Physics}
MSC:
| 82C22 | Interacting particle systems in time-dependent statistical mechanics |
| 82B30 | Statistical thermodynamics |
| 81V70 | Many-body theory; quantum Hall effect |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 81S30 | Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics |
| 35Q40 | PDEs in connection with quantum mechanics |
Keywords:
many-body Hamiltonians; multi-particle (potential) interaction; Wigner measures approach; nonlinear Hartree field equationReferences:
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