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Journal of the European Mathematical Society


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Volume 22, Issue 7, 2020, pp. 2331–2403
DOI: 10.4171/JEMS/966

Published online: 2020-04-22

The excitation spectrum of Bose gases interacting through singular potentials

Chiara Boccato[1], Christian Brennecke[2], Serena Cenatiempo[3] and Benjamin Schlein[4]

(1) Universität Zürich, Switzerland and IST Austria, Klosterneuburg, Austria
(2) Universität Zürich, Switzerland
(3) Gran Sasso Science Institute, L'Aquila, Italy
(4) Universität Zürich, Switzerland

We consider systems of $N$ bosons in a box of volume one, interacting through a repulsive two-body potential of the form $\kappa N^{3\beta-1} V(N^\beta x)$. For all $0 < \beta < 1$, and for sufficiently small coupling constant $\kappa > 0$, we establish the validity of Bogolyubov theory, identifying the ground state energy and the low-lying excitation spectrum up to errors that vanish in the limit of large $N$.

Keywords: Excitation spectrum, Bose gase, Bose–Einstein condensation, Bogolyubov theory

Boccato Chiara, Brennecke Christian, Cenatiempo Serena, Schlein Benjamin: The excitation spectrum of Bose gases interacting through singular potentials. J. Eur. Math. Soc. 22 (2020), 2331-2403. doi: 10.4171/JEMS/966