{"abstract":[{"text":"We prove rigorously that the one-particle density matrix of three dimensional interacting Bose systems with a short-scale repulsive pair interaction converges to the solution of the cubic non-linear Schrödinger equation in a suitable scaling limit. The result is extended to k-particle density matrices for all positive integer k. ","lang":"eng"}],"_id":"2749","publication":"Inventiones Mathematicae","date_updated":"2019-04-26T07:22:19Z","quality_controlled":0,"page":"515 - 614","issue":"3","doi":"10.1007/s00222-006-0022-1","author":[{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","full_name":"László Erdös"},{"first_name":"Benjamin","full_name":"Schlein, Benjamin","last_name":"Schlein"},{"full_name":"Yau, Horng-Tzer","last_name":"Yau","first_name":"Horng"}],"publist_id":"4143","citation":{"short":"L. Erdös, B. Schlein, H. Yau, Inventiones Mathematicae 167 (2007) 515–614.","ama":"Erdös L, Schlein B, Yau H. Derivation of the cubic non linear Schrödinger equation from quantum dynamics of many body systems. <i>Inventiones Mathematicae</i>. 2007;167(3):515-614. doi:<a href=\"https://doi.org/10.1007/s00222-006-0022-1\">10.1007/s00222-006-0022-1</a>","ista":"Erdös L, Schlein B, Yau H. 2007. Derivation of the cubic non linear Schrödinger equation from quantum dynamics of many body systems. Inventiones Mathematicae. 167(3), 515–614.","ieee":"L. Erdös, B. Schlein, and H. Yau, “Derivation of the cubic non linear Schrödinger equation from quantum dynamics of many body systems,” <i>Inventiones Mathematicae</i>, vol. 167, no. 3. Springer, pp. 515–614, 2007.","mla":"Erdös, László, et al. “Derivation of the Cubic Non Linear Schrödinger Equation from Quantum Dynamics of Many Body Systems.” <i>Inventiones Mathematicae</i>, vol. 167, no. 3, Springer, 2007, pp. 515–614, doi:<a href=\"https://doi.org/10.1007/s00222-006-0022-1\">10.1007/s00222-006-0022-1</a>.","apa":"Erdös, L., Schlein, B., &#38; Yau, H. (2007). Derivation of the cubic non linear Schrödinger equation from quantum dynamics of many body systems. <i>Inventiones Mathematicae</i>. Springer. <a href=\"https://doi.org/10.1007/s00222-006-0022-1\">https://doi.org/10.1007/s00222-006-0022-1</a>","chicago":"Erdös, László, Benjamin Schlein, and Horng Yau. “Derivation of the Cubic Non Linear Schrödinger Equation from Quantum Dynamics of Many Body Systems.” <i>Inventiones Mathematicae</i>. Springer, 2007. <a href=\"https://doi.org/10.1007/s00222-006-0022-1\">https://doi.org/10.1007/s00222-006-0022-1</a>."},"intvolume":"       167","status":"public","title":"Derivation of the cubic non linear Schrödinger equation from quantum dynamics of many body systems","extern":1,"publication_status":"published","date_created":"2018-12-11T11:59:24Z","date_published":"2007-03-01T00:00:00Z","type":"review","year":"2007","volume":167,"publisher":"Springer","day":"01","month":"03"}