Diagonalizing Bose Gases in the Gross-Pitaevskii Regime and Beyond.

We present a novel approach to the Bogoliubov theory of dilute Bose gases, allowing for an elementary derivation of the celebrated Lee-Huang-Yang formula in the Gross-Pitaevskii regime. Furthermore, we identify the low lying excitation spectrum beyond the Gross-Pitaevskii scaling, extending a recent result (Brennecke et al. in Rev Math Phys 34, 2022) to significantly more singular scaling regimes.

Characterisation of gradient flows for a given functional.

Let be a vector field and be a co-vector field on a smooth manifold . Does there exist a smooth Riemannian metric on such that ? The main result of this note gives necessary and sufficient conditions for this to be true. As an application of this result we provide a gradient-flow characterisation for dissipative quantum systems.