[{"publication":"Archive for Rational Mechanics and Analysis","volume":179,"title":"Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons","day":"01","publication_status":"published","month":"02","publisher":"Springer","quality_controlled":0,"issue":"2","intvolume":" 179","extern":1,"page":"265 - 283","doi":"10.1007/s00205-005-0388-z","date_updated":"2019-04-26T07:22:19Z","publist_id":"4147","date_created":"2018-12-11T11:59:22Z","citation":{"ama":"Elgart A, Erdös L, Schlein B, Yau H. Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons. *Archive for Rational Mechanics and Analysis*. 2006;179(2):265-283. doi:10.1007/s00205-005-0388-z","chicago":"Elgart, Alexander, László Erdös, Benjamin Schlein, and Horng Yau. “Gross-Pitaevskii Equation as the Mean Field Limit of Weakly Coupled Bosons.” *Archive for Rational Mechanics and Analysis* 179, no. 2 (2006): 265–83. https://doi.org/10.1007/s00205-005-0388-z.","ista":"Elgart A, Erdös L, Schlein B, Yau H. 2006. Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons. Archive for Rational Mechanics and Analysis. 179(2), 265–283.","short":"A. Elgart, L. Erdös, B. Schlein, H. Yau, Archive for Rational Mechanics and Analysis 179 (2006) 265–283.","ieee":"A. Elgart, L. Erdös, B. Schlein, and H. Yau, “Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons,” *Archive for Rational Mechanics and Analysis*, vol. 179, no. 2, pp. 265–283, 2006.","mla":"Elgart, Alexander, et al. “Gross-Pitaevskii Equation as the Mean Field Limit of Weakly Coupled Bosons.” *Archive for Rational Mechanics and Analysis*, vol. 179, no. 2, Springer, 2006, pp. 265–83, doi:10.1007/s00205-005-0388-z.","apa":"Elgart, A., Erdös, L., Schlein, B., & Yau, H. (2006). Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons. *Archive for Rational Mechanics and Analysis*, *179*(2), 265–283. https://doi.org/10.1007/s00205-005-0388-z"},"_id":"2745","year":"2006","abstract":[{"text":"We consider the dynamics of N boson systems interacting through a pair potential N -1 V a (x i -x j ) where V a (x)=a -3 V(x/a). We denote the solution to the N-particle Schrödinger equation by Ψ N, t . Recall that the Gross-Pitaevskii (GP) equation is a nonlinear Schrödinger equation and the GP hierarchy is an infinite BBGKY hierarchy of equations so that if u t solves the GP equation, then the family of k-particle density matrices [InlineMediaObject not available: see fulltext.] solves the GP hierarchy. Under the assumption that a = Nε for 0 < ε < 3/5, we prove that as N→∞ the limit points of the k-particle density matrices of Ψ N, t are solutions of the GP hierarchy with the coupling constant in the nonlinear term of the GP equation given by ∫ V (x)dx. The uniqueness of the solutions of this hierarchy remains an open question.","lang":"eng"}],"type":"journal_article","author":[{"last_name":"Elgart","full_name":"Elgart, Alexander","first_name":"Alexander"},{"orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"László Erdös"},{"full_name":"Schlein, Benjamin","first_name":"Benjamin","last_name":"Schlein"},{"full_name":"Yau, Horng-Tzer","first_name":"Horng","last_name":"Yau"}],"date_published":"2006-02-01T00:00:00Z","status":"public"}]