Bose-Einstein condensation for two dimensional bosons in the Gross-Pitaevskii regime

We consider systems of N bosons trapped on the two-dimensional unit torus, in the Gross-Pitaevskii regime, where the scattering length of the repulsive interaction is exponentially small in the number of particles. We show that low-energy states exhibit complete Bose-Einstein condensation, with almost optimal bounds on the number of orthogonal excitations.Comment: 72 pages, improved rate of condensatio

The Excitation Spectrum of Two-Dimensional Bose Gases in the Gross–Pitaevskii Regime

We consider a system of N bosons, in the two-dimensional unit torus. We assume particles to interact through a repulsive two-body potential, with a scattering length that is exponentially small in N (Gross–Pitaevskii regime). In this setting, we establish the validity of the predictions of Bogoliubov theory, determining the ground state energy of the Hamilton operator and its low-energy excitation spectrum, up to errors that vanish in the limit N→ ∞

Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime

We consider systems of bosons trapped in a box, in the Gross-Pitaevskii regime. We show that low-energy states exhibit complete Bose-Einstein condensation with an optimal bound on the number of orthogonal excitations. This extends recent results obtained in \cite{BBCS1}, removing the assumption of small interaction potential.Comment: 99 pages, typos correcte

A Second Order Upper Bound for the Ground State Energy of a Hard-Sphere Gas in the Gross–Pitaevskii Regime

We prove an upper bound for the ground state energy of a Bose gas consisting of N hard spheres with radius a/N, moving in the three-dimensional unit torus Λ. Our estimate captures the correct asymptotics of the ground state energy, up to errors that vanish in the limit N→∞. The proof is based on the construction of an appropriate trial state, given by the product of a Jastrow factor (describing two-particle correlations on short scales) and of a wave function constructed through a (generalized) Bogoliubov transformation, generating orthogonal excitations of the Bose–Einstein condensate and describing correlations on large scales

Low dimensional interacting bosons

The research leading to my PhD thesis results has received funding from the European Research Council under the European Union’s Seventh Framework Programme ERC Starting Grant CoMBoS (grant agreement no 239694

Bose–Einstein condensation for two dimensional bosons in the Gross–Pitaevskii regime

We consider systems of N bosons trapped on the two-dimensional unit torus, in the Gross-Pitaevskii regime, where the scattering length of the repulsive interaction is exponentially small in the number of particles. We show that low-energy states exhibit complete Bose–Einstein condensation, with almost optimal bounds on the number of orthogonal excitations