@article{7413,
  abstract     = {We consider Bose gases consisting of N particles trapped in a box with volume one and interacting through a repulsive potential with scattering length of order N−1 (Gross–Pitaevskii regime). We determine the ground state energy and the low-energy excitation spectrum, up to errors vanishing as N→∞. Our results confirm Bogoliubov’s predictions.},
  author       = {Boccato, Chiara and Brennecke, Christian and Cenatiempo, Serena and Schlein, Benjamin},
  issn         = {1871-2509},
  journal      = {Acta Mathematica},
  number       = {2},
  pages        = {219--335},
  publisher    = {International Press of Boston},
  title        = {{Bogoliubov theory in the Gross–Pitaevskii limit}},
  doi          = {10.4310/acta.2019.v222.n2.a1},
  volume       = {222},
  year         = {2019},
}

@article{8494,
  abstract     = {We prove a form of Arnold diffusion in the a-priori stable case. Let
H0(p)+ϵH1(θ,p,t),θ∈Tn,p∈Bn,t∈T=R/T,
be a nearly integrable system of arbitrary degrees of freedom n⩾2 with a strictly convex H0. We show that for a “generic” ϵH1, there exists an orbit (θ,p) satisfying
∥p(t)−p(0)∥>l(H1)>0,
where l(H1) is independent of ϵ. The diffusion orbit travels along a codimension-1 resonance, and the only obstruction to our construction is a finite set of additional resonances.

For the proof we use a combination of geometric and variational methods, and manage to adapt tools which have recently been developed in the a-priori unstable case.},
  author       = {Bernard, Patrick and Kaloshin, Vadim and Zhang, Ke},
  issn         = {0001-5962},
  journal      = {Acta Mathematica},
  number       = {1},
  pages        = {1--79},
  publisher    = {Institut Mittag-Leffler},
  title        = {{Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders}},
  doi          = {10.1007/s11511-016-0141-5},
  volume       = {217},
  year         = {2016},
}