[{"arxiv":1,"abstract":[{"text":"We consider Bose gases consisting of N particles trapped in a box with volume one and interacting through a repulsive potential with scattering length of order N−1 (Gross–Pitaevskii regime). We determine the ground state energy and the low-energy excitation spectrum, up to errors vanishing as N→∞. Our results confirm Bogoliubov’s predictions.","lang":"eng"}],"publisher":"International Press of Boston","department":[{"_id":"RoSe"}],"title":"Bogoliubov theory in the Gross–Pitaevskii limit","publication":"Acta Mathematica","oa_version":"Preprint","date_created":"2020-01-30T09:30:41Z","article_type":"original","external_id":{"arxiv":["1801.01389"],"isi":["000495865300001"]},"issue":"2","status":"public","oa":1,"publication_identifier":{"issn":["0001-5962"],"eissn":["1871-2509"]},"citation":{"mla":"Boccato, Chiara, et al. “Bogoliubov Theory in the Gross–Pitaevskii Limit.” <i>Acta Mathematica</i>, vol. 222, no. 2, International Press of Boston, 2019, pp. 219–335, doi:<a href=\"https://doi.org/10.4310/acta.2019.v222.n2.a1\">10.4310/acta.2019.v222.n2.a1</a>.","ista":"Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2019. Bogoliubov theory in the Gross–Pitaevskii limit. Acta Mathematica. 222(2), 219–335.","short":"C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Acta Mathematica 222 (2019) 219–335.","ama":"Boccato C, Brennecke C, Cenatiempo S, Schlein B. Bogoliubov theory in the Gross–Pitaevskii limit. <i>Acta Mathematica</i>. 2019;222(2):219-335. doi:<a href=\"https://doi.org/10.4310/acta.2019.v222.n2.a1\">10.4310/acta.2019.v222.n2.a1</a>","apa":"Boccato, C., Brennecke, C., Cenatiempo, S., &#38; Schlein, B. (2019). Bogoliubov theory in the Gross–Pitaevskii limit. <i>Acta Mathematica</i>. International Press of Boston. <a href=\"https://doi.org/10.4310/acta.2019.v222.n2.a1\">https://doi.org/10.4310/acta.2019.v222.n2.a1</a>","ieee":"C. Boccato, C. Brennecke, S. Cenatiempo, and B. Schlein, “Bogoliubov theory in the Gross–Pitaevskii limit,” <i>Acta Mathematica</i>, vol. 222, no. 2. International Press of Boston, pp. 219–335, 2019.","chicago":"Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein. “Bogoliubov Theory in the Gross–Pitaevskii Limit.” <i>Acta Mathematica</i>. International Press of Boston, 2019. <a href=\"https://doi.org/10.4310/acta.2019.v222.n2.a1\">https://doi.org/10.4310/acta.2019.v222.n2.a1</a>."},"type":"journal_article","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","page":"219-335","volume":222,"year":"2019","_id":"7413","date_updated":"2023-09-06T15:24:31Z","doi":"10.4310/acta.2019.v222.n2.a1","article_processing_charge":"No","author":[{"id":"342E7E22-F248-11E8-B48F-1D18A9856A87","full_name":"Boccato, Chiara","last_name":"Boccato","first_name":"Chiara"},{"last_name":"Brennecke","first_name":"Christian","full_name":"Brennecke, Christian"},{"first_name":"Serena","last_name":"Cenatiempo","full_name":"Cenatiempo, Serena"},{"full_name":"Schlein, Benjamin","last_name":"Schlein","first_name":"Benjamin"}],"date_published":"2019-06-07T00:00:00Z","quality_controlled":"1","scopus_import":"1","day":"07","language":[{"iso":"eng"}],"isi":1,"month":"06","publication_status":"published","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1801.01389"}],"intvolume":"       222"},{"oa_version":"None","date_created":"2020-09-18T10:46:07Z","publisher":"Institut Mittag-Leffler","title":"Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders","publication":"Acta Mathematica","extern":"1","quality_controlled":"1","abstract":[{"lang":"eng","text":"We prove a form of Arnold diffusion in the a-priori stable case. Let\r\nH0(p)+ϵH1(θ,p,t),θ∈Tn,p∈Bn,t∈T=R/T,\r\nbe a nearly integrable system of arbitrary degrees of freedom n⩾2 with a strictly convex H0. We show that for a “generic” ϵH1, there exists an orbit (θ,p) satisfying\r\n∥p(t)−p(0)∥>l(H1)>0,\r\nwhere l(H1) is independent of ϵ. The diffusion orbit travels along a codimension-1 resonance, and the only obstruction to our construction is a finite set of additional resonances.\r\n\r\nFor the proof we use a combination of geometric and variational methods, and manage to adapt tools which have recently been developed in the a-priori unstable case."}],"date_updated":"2021-01-12T08:19:39Z","doi":"10.1007/s11511-016-0141-5","article_processing_charge":"No","date_published":"2016-09-28T00:00:00Z","author":[{"full_name":"Bernard, Patrick","last_name":"Bernard","first_name":"Patrick"},{"last_name":"Kaloshin","orcid":"0000-0002-6051-2628","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim"},{"full_name":"Zhang, Ke","last_name":"Zhang","first_name":"Ke"}],"publication_status":"published","year":"2016","intvolume":"       217","_id":"8494","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"1-79","volume":217,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0001-5962"]},"month":"09","citation":{"ieee":"P. Bernard, V. Kaloshin, and K. Zhang, “Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders,” <i>Acta Mathematica</i>, vol. 217, no. 1. Institut Mittag-Leffler, pp. 1–79, 2016.","chicago":"Bernard, Patrick, Vadim Kaloshin, and Ke Zhang. “Arnold Diffusion in Arbitrary Degrees of Freedom and Normally Hyperbolic Invariant Cylinders.” <i>Acta Mathematica</i>. Institut Mittag-Leffler, 2016. <a href=\"https://doi.org/10.1007/s11511-016-0141-5\">https://doi.org/10.1007/s11511-016-0141-5</a>.","apa":"Bernard, P., Kaloshin, V., &#38; Zhang, K. (2016). Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders. <i>Acta Mathematica</i>. Institut Mittag-Leffler. <a href=\"https://doi.org/10.1007/s11511-016-0141-5\">https://doi.org/10.1007/s11511-016-0141-5</a>","ama":"Bernard P, Kaloshin V, Zhang K. Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders. <i>Acta Mathematica</i>. 2016;217(1):1-79. doi:<a href=\"https://doi.org/10.1007/s11511-016-0141-5\">10.1007/s11511-016-0141-5</a>","mla":"Bernard, Patrick, et al. “Arnold Diffusion in Arbitrary Degrees of Freedom and Normally Hyperbolic Invariant Cylinders.” <i>Acta Mathematica</i>, vol. 217, no. 1, Institut Mittag-Leffler, 2016, pp. 1–79, doi:<a href=\"https://doi.org/10.1007/s11511-016-0141-5\">10.1007/s11511-016-0141-5</a>.","short":"P. Bernard, V. Kaloshin, K. Zhang, Acta Mathematica 217 (2016) 1–79.","ista":"Bernard P, Kaloshin V, Zhang K. 2016. Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders. Acta Mathematica. 217(1), 1–79."},"article_type":"original","day":"28","issue":"1","status":"public"}]