Acta Mathematica

Volume 222 (2019)

Number 2

Bogoliubov theory in the Gross–Pitaevskii limit

Pages: 219 – 335



Chiara Boccato (Institute of Science and Technology, Klosterneuburg, Austria)

Christian Brennecke (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)

Serena Cenatiempo (Gran Sasso Science Institute, L’Aquila, Italy)

Benjamin Schlein (Institute of Mathematics, University of Zürich, Switzerland)


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 $N \to \infty$. Our results confirm Bogoliubov’s predictions.

Received 28 February 2018

Accepted 7 January 2019

Published 7 June 2019