MCQM22 Third School and Workshop

Mathematical Challenges in Quantum Mechanics

Como, Italy -- June 13 - 18, 2022

Serena Cenatiempo

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, modelling a trapped Bose gas where both the quantum and thermal motions are frozen in one direction. 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 scaling limit - which provides a first example of a dilute regime in which peculiarities of two-dimensional systems can be observed - 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 → ∞.

Based on joint works with Cristina Caraci and Benjamin Schlein.