JournalsjemsVol. 22, No. 7pp. 2331–2403

The excitation spectrum of Bose gases interacting through singular potentials

  • Chiara Boccato

    Universität Zürich, Switzerland and IST Austria, Klosterneuburg, Austria
  • Christian Brennecke

    Universität Zürich, Switzerland
  • Serena Cenatiempo

    Gran Sasso Science Institute, L'Aquila, Italy
  • Benjamin Schlein

    Universität Zürich, Switzerland
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Abstract

We consider systems of NN bosons in a box of volume one, interacting through a repulsive two-body potential of the form κN3β1V(Nβx)\kappa N^{3\beta-1} V(N^\beta x). For all 0<β<10 < \beta < 1, and for sufficiently small coupling constant κ>0\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 NN.

Cite this article

Chiara Boccato, Christian Brennecke, Serena Cenatiempo, Benjamin Schlein, The excitation spectrum of Bose gases interacting through singular potentials. J. Eur. Math. Soc. 22 (2020), no. 7, pp. 2331–2403

DOI 10.4171/JEMS/966