Optimal Rate for Bose–Einstein Condensation in the Gross–Pitaevskii Regime

  • Chiara Boccato
  • Christian Brennecke
  • Serena Cenatiempo
  • Benjamin SchleinEmail author


We consider systems of bosons trapped in a box, in the Gross–Pitaevskii regime. We show that low-energy states exhibit complete Bose–Einstein condensation with an optimal bound on the number of orthogonal excitations. This extends recent results obtained in Boccato et al. (Commun Math Phys 359(3):975–1026, 2018), removing the assumption of small interaction potential.



We would like to thank P. T. Nam and R. Seiringer for several useful discussions and for suggesting us to use the localization techniques from [9]. C. Boccato has received funding from the European Research Council (ERC) under the programme Horizon 2020 (Grant Agreement 694227). B. Schlein gratefully acknowledges support from the NCCR SwissMAP and from the Swiss National Foundation of Science (Grant No. 200020_1726230) through the SNF Grant “Dynamical and energetic properties of Bose–Einstein condensates”.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Science and Technology AustriaKlosterneuburgAustria
  2. 2.Department of MathematicsHarvard UniversityCambridgeUSA
  3. 3.Gran Sasso Science InstituteL’AquilaItaly
  4. 4.Institute of MathematicsUniversity of ZurichZurichSwitzerland

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