{"title":"Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons","doi":"10.1007/s00205-005-0388-z","intvolume":"       179","quality_controlled":0,"date_published":"2006-02-01T00:00:00Z","volume":179,"status":"public","page":"265 - 283","year":"2006","abstract":[{"lang":"eng","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 &lt; ε &lt; 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."}],"author":[{"full_name":"Elgart, Alexander","first_name":"Alexander","last_name":"Elgart"},{"last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"László Erdös"},{"first_name":"Benjamin","full_name":"Schlein, Benjamin","last_name":"Schlein"},{"last_name":"Yau","full_name":"Yau, Horng-Tzer","first_name":"Horng"}],"date_created":"2018-12-11T11:59:22Z","publist_id":"4147","publication_status":"published","day":"01","month":"02","publication":"Archive for Rational Mechanics and Analysis","extern":1,"date_updated":"2021-01-12T06:59:25Z","type":"journal_article","_id":"2745","issue":"2","citation":{"mla":"Elgart, Alexander, et al. “Gross-Pitaevskii Equation as the Mean Field Limit of Weakly Coupled Bosons.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 179, no. 2, Springer, 2006, pp. 265–83, doi:<a href=\"https://doi.org/10.1007/s00205-005-0388-z\">10.1007/s00205-005-0388-z</a>.","ama":"Elgart A, Erdös L, Schlein B, Yau H. Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons. <i>Archive for Rational Mechanics and Analysis</i>. 2006;179(2):265-283. doi:<a href=\"https://doi.org/10.1007/s00205-005-0388-z\">10.1007/s00205-005-0388-z</a>","ieee":"A. Elgart, L. Erdös, B. Schlein, and H. Yau, “Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 179, no. 2. Springer, pp. 265–283, 2006.","apa":"Elgart, A., Erdös, L., Schlein, B., &#38; Yau, H. (2006). Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons. <i>Archive for Rational Mechanics and Analysis</i>. Springer. <a href=\"https://doi.org/10.1007/s00205-005-0388-z\">https://doi.org/10.1007/s00205-005-0388-z</a>","short":"A. Elgart, L. Erdös, B. Schlein, H. Yau, Archive for Rational Mechanics and Analysis 179 (2006) 265–283.","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.","chicago":"Elgart, Alexander, László Erdös, Benjamin Schlein, and Horng Yau. “Gross-Pitaevskii Equation as the Mean Field Limit of Weakly Coupled Bosons.” <i>Archive for Rational Mechanics and Analysis</i>. Springer, 2006. <a href=\"https://doi.org/10.1007/s00205-005-0388-z\">https://doi.org/10.1007/s00205-005-0388-z</a>."},"publisher":"Springer"}