{"abstract":[{"lang":"eng","text":"We consider the time evolution of N bosonic particles interacting via a mean field Coulomb potential. Suppose the initial state is a product wavefunction. We show that at any finite time the correlation functions factorize in the limit N → ∞. Furthermore, the limiting one particle density matrix satisfies the nonlinear Hartree equation. The key ingredients are the uniqueness of the BBGKY hierarchy for the correlation functions and a new apriori estimate for the many-body Schrödinger equations."}],"date_published":"2001-11-01T00:00:00Z","publication_identifier":{"issn":["1095-0761"]},"date_updated":"2023-05-16T12:12:41Z","doi":"10.48550/arXiv.math-ph/0111042","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","oa_version":"Published Version","article_processing_charge":"No","oa":1,"author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","last_name":"Erdös","full_name":"Erdös, László","first_name":"László"},{"first_name":"Horng","full_name":"Yau, Horng","last_name":"Yau"}],"intvolume":"         5","issue":"6","type":"journal_article","scopus_import":"1","day":"01","volume":5,"article_type":"original","status":"public","publication":"Advances in Theoretical and Mathematical Physics","external_id":{"arxiv":["math-ph/0111042"]},"_id":"2736","date_created":"2018-12-11T11:59:20Z","page":"1169 - 1205","title":"Derivation of the nonlinear Schrödinger equation from a many body Coulomb system","quality_controlled":"1","month":"11","language":[{"iso":"eng"}],"publication_status":"published","main_file_link":[{"url":"http://arxiv.org/abs/math-ph/0111042","open_access":"1"}],"publist_id":"4156","publisher":"International Press","citation":{"ama":"Erdös L, Yau H. Derivation of the nonlinear Schrödinger equation from a many body Coulomb system. <i>Advances in Theoretical and Mathematical Physics</i>. 2001;5(6):1169-1205. doi:<a href=\"https://doi.org/10.48550/arXiv.math-ph/0111042\">10.48550/arXiv.math-ph/0111042</a>","short":"L. Erdös, H. Yau, Advances in Theoretical and Mathematical Physics 5 (2001) 1169–1205.","mla":"Erdös, László, and Horng Yau. “Derivation of the Nonlinear Schrödinger Equation from a Many Body Coulomb System.” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 5, no. 6, International Press, 2001, pp. 1169–205, doi:<a href=\"https://doi.org/10.48550/arXiv.math-ph/0111042\">10.48550/arXiv.math-ph/0111042</a>.","ieee":"L. Erdös and H. Yau, “Derivation of the nonlinear Schrödinger equation from a many body Coulomb system,” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 5, no. 6. International Press, pp. 1169–1205, 2001.","ista":"Erdös L, Yau H. 2001. Derivation of the nonlinear Schrödinger equation from a many body Coulomb system. Advances in Theoretical and Mathematical Physics. 5(6), 1169–1205.","chicago":"Erdös, László, and Horng Yau. “Derivation of the Nonlinear Schrödinger Equation from a Many Body Coulomb System.” <i>Advances in Theoretical and Mathematical Physics</i>. International Press, 2001. <a href=\"https://doi.org/10.48550/arXiv.math-ph/0111042\">https://doi.org/10.48550/arXiv.math-ph/0111042</a>.","apa":"Erdös, L., &#38; Yau, H. (2001). Derivation of the nonlinear Schrödinger equation from a many body Coulomb system. <i>Advances in Theoretical and Mathematical Physics</i>. International Press. <a href=\"https://doi.org/10.48550/arXiv.math-ph/0111042\">https://doi.org/10.48550/arXiv.math-ph/0111042</a>"},"extern":"1","year":"2001"}