The quintic NLS as the mean field limit of a boson gas with three-body interactions
By Thomas Chen, Natavsa Pavlovi'c. 2008
132 citations recorded by the source corpus.
We investigate the dynamics of a boson gas with three-body interactions in dimensions d=1,2. We prove that in the limit of infinite particle number, the BBGKY hierarchy of k-particle marginals converges to a limiting (Gross–Pitaevskii (GP)) hierarchy for which we prove existence and uniqueness of solutions. Factorized solutions of the GP hierarchy are shown to be determined by solutions of a quintic nonlinear Schrodinger equation. Our proof is based on, and extends, methods of Erdos–Schlein–Yau, Klainerman–Machedon, and Kirkpatrick–Schlein–Staffilani.
Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/a8d57a6943b82f79e3d0f2c0eebcbbc56da3e956
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In Atomic and Molecular Physics, and Optics
- Niels Benedikter
- M. Porta
- B. Schlein
- P. Pickl
- Igor Rodnianski
- E. Lenzmann
- Clément Mouhot
- M. Machedon
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Effective Evolution Equations from Quantum Dynamics (2015, methodology): “It is also possible to start from Hamiltonians with three-body interactions; in this case, the evolution can be approximated by a quintic nonlinear Schrödinger equation; see [23, 18].”