{"oa":1,"oa_version":"Published Version","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_created":"2019-11-25T08:08:02Z","publisher":"Springer Nature","scopus_import":"1","quality_controlled":"1","title":"Derivation of the time dependent Gross–Pitaevskii equation in two dimensions","status":"public","file":[{"file_id":"7101","file_size":884469,"date_created":"2019-11-25T08:11:11Z","date_updated":"2020-07-14T12:47:49Z","content_type":"application/pdf","file_name":"2019_CommMathPhys_Jeblick.pdf","creator":"dernst","access_level":"open_access","relation":"main_file","checksum":"cd283b475dd739e04655315abd46f528"}],"type":"journal_article","license":"https://creativecommons.org/licenses/by/4.0/","day":"08","article_processing_charge":"Yes (via OA deal)","month":"11","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_updated":"2023-09-06T10:47:43Z","publication_status":"published","date_published":"2019-11-08T00:00:00Z","issue":"1","department":[{"_id":"RoSe"}],"abstract":[{"text":"We present microscopic derivations of the defocusing two-dimensional cubic nonlinear Schrödinger equation and the Gross–Pitaevskii equation starting froman interacting N-particle system of bosons. We consider the interaction potential to be given either by Wβ(x)=N−1+2βW(Nβx), for any β>0, or to be given by VN(x)=e2NV(eNx), for some spherical symmetric, nonnegative and compactly supported W,V∈L∞(R2,R). In both cases we prove the convergence of the reduced density corresponding to the exact time evolution to the projector onto the solution of the corresponding nonlinear Schrödinger equation in trace norm. For the latter potential VN we show that it is crucial to take the microscopic structure of the condensate into account in order to obtain the correct dynamics.","lang":"eng"}],"intvolume":"       372","volume":372,"year":"2019","acknowledgement":"OA fund by IST Austria","file_date_updated":"2020-07-14T12:47:49Z","isi":1,"ddc":["510"],"project":[{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"page":"1-69","doi":"10.1007/s00220-019-03599-x","publication":"Communications in Mathematical Physics","has_accepted_license":"1","author":[{"last_name":"Jeblick","first_name":"Maximilian","full_name":"Jeblick, Maximilian"},{"last_name":"Leopold","first_name":"Nikolai K","id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","full_name":"Leopold, Nikolai K","orcid":"0000-0002-0495-6822"},{"last_name":"Pickl","first_name":"Peter","full_name":"Pickl, Peter"}],"external_id":{"isi":["000495193700002"]},"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"ec_funded":1,"article_type":"original","citation":{"ieee":"M. Jeblick, N. K. Leopold, and P. Pickl, “Derivation of the time dependent Gross–Pitaevskii equation in two dimensions,” <i>Communications in Mathematical Physics</i>, vol. 372, no. 1. Springer Nature, pp. 1–69, 2019.","mla":"Jeblick, Maximilian, et al. “Derivation of the Time Dependent Gross–Pitaevskii Equation in Two Dimensions.” <i>Communications in Mathematical Physics</i>, vol. 372, no. 1, Springer Nature, 2019, pp. 1–69, doi:<a href=\"https://doi.org/10.1007/s00220-019-03599-x\">10.1007/s00220-019-03599-x</a>.","short":"M. Jeblick, N.K. Leopold, P. Pickl, Communications in Mathematical Physics 372 (2019) 1–69.","ama":"Jeblick M, Leopold NK, Pickl P. Derivation of the time dependent Gross–Pitaevskii equation in two dimensions. <i>Communications in Mathematical Physics</i>. 2019;372(1):1-69. doi:<a href=\"https://doi.org/10.1007/s00220-019-03599-x\">10.1007/s00220-019-03599-x</a>","chicago":"Jeblick, Maximilian, Nikolai K Leopold, and Peter Pickl. “Derivation of the Time Dependent Gross–Pitaevskii Equation in Two Dimensions.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2019. <a href=\"https://doi.org/10.1007/s00220-019-03599-x\">https://doi.org/10.1007/s00220-019-03599-x</a>.","apa":"Jeblick, M., Leopold, N. K., &#38; Pickl, P. (2019). Derivation of the time dependent Gross–Pitaevskii equation in two dimensions. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-019-03599-x\">https://doi.org/10.1007/s00220-019-03599-x</a>","ista":"Jeblick M, Leopold NK, Pickl P. 2019. Derivation of the time dependent Gross–Pitaevskii equation in two dimensions. Communications in Mathematical Physics. 372(1), 1–69."},"language":[{"iso":"eng"}],"_id":"7100"}