PhD Defense Lukas Junge
TITLE: Energies of Dilute Bose Gases
Abstract:
In this thesis, we study the Dilute Bose Gas under various assumptions in two and three dimensions. In three dimensions, we establish a new lower bound for the free energy at low temperature, valid under stronger interactions than previously treated. In two dimensions, we prove the full two dimensional analogue Lee–Huang–Yang formula for the ground state energy, confirming its universality, and derive an upper bound for the corresponding free energy expansion, consistent with Bogoliubov theory despite the absence of Bose–Einstein condensation at positive temperature.
Beyond two-body interactions, we resolve the leading-order ground state energy of a Bose gas with three-body hardcore interactions by providing a sharp upper bound, matching existing lower bounds.
Finally, we derive Hartree theory for two dimensional Bose gases with attractive interactions in an almost Gross-Pitaevskii regime, proving stability and convergence to the nonlinear Schrödinger functional
Link to Hybrid defense: Zoom : https://ucph-ku.zoom.us/j/5493618890?pwd=a0E3U3dsd0dOZVJhRWlkV3owcG9hdz09
Advisor: Søren Fournais, University of Copenhagen, Copenhagen, Denmark
Assessment committee:
Jan Philip Solovej (Chair), University of Copenhagen, Copenhagen, Denmark
Phan Thành Nam, Ludwig-Maximilians-Universität München, Munich, Germany
Robert Seiringer, Institute of Science and Technology Austria, Klosterneuburg, Austria