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## Seminar Analysis and Mathematical Physics: Lea Bossmann (IST Austria)

**Asymptotic expansion of low-energy excitations for weakly interacting bosons**

Abstract.

We consider a system of N bosons in the mean-field scaling regime in an external trapping potential. We derive an asymptotic expansion of the low-energy eigenstates and the corresponding energies, which provides corrections to Bogoliubov theory to any order in 1/N. We show that the structure of the ground state and of the non-degenerate low-energy eigenstates is preserved by the dynamics if

the external trap is switched off. This talk is based on joint works with Sören Petrat, Peter Pickl, Robert Seiringer, and Avy Soffer (arXiv:1912.11004 and arXiv:2006.09825).

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