The excitation spectrum of two dimensional Bose gases in the Gross-Pitaevskii regime

Abstract

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 $N\to \infty$.

51 pages, typos corrected

References in corpus (5)

• Ground state energy of the two-dimensional weakly interacting Bose gas: First correction beyond Bogoliubov theory
• Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime
• Bose-Einstein Condensation with Optimal Rate for Trapped Bosons in the Gross-Pitaevskii Regime
• Excitation Spectrum for Bose Gases beyond the Gross-Pitaevskii Regime
• Renormalization theory of a two dimensional Bose gas: quantum critical point and quasi-condensed state

Cited by in corpus (8)

• Upper bound for the grand canonical free energy of the Bose gas in the Gross-Pitaevskii limit
• Quantum Fluctuations of Many-Body Dynamics around the Gross-Pitaevskii Equation
• Upper bound for the grand canonical free energy of the Bose gas in the Gross-Pitaevskii limit for general interaction potentials
• Third order corrections to the ground state energy of a Bose gas in the Gross-Pitaevskii regime
• A Short Proof of Bose-Einstein Condensation in the Gross-Pitaevskii Regime and Beyond
• Lower bounds on the energy of the Bose gas
• The excitation spectrum of a Bose gas with an impurity in the Gross-Pitaevskii regime
• The Second Order 2D Behaviors of a 3D Bose Gases in the Gross-Pitaevskii Regime