The excitation spectrum of Bose gases interacting through singular potentials
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, id...
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Veröffentlicht in: | Journal of the European Mathematical Society : JEMS 2020-01, Vol.22 (7), p.2331-2403 |
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Hauptverfasser: | , , , |
Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | 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 $N$. |
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ISSN: | 1435-9855 1435-9863 |
DOI: | 10.4171/JEMS/966 |