Aarhus-Copenhagen Research Group Day
QMATH organizes a Copenhagen-Aarhus Day with Søren Fournais and his research group.
Schedule:
| 10:00 | Arrival and welcome |
| 10:30-11:15 | Speaker: Johannes Agerskov Title: The ground state energy of dilute 1D many-body quantum systems Abstract: In this talk we consider a dilute gas of 1D bosons interacting through a general, repulsive two-body potential. We will show that the ground state energy admits a first order expansion in the 1D diluteness parameter, where the zeroth-order term coincides with the free Fermi ground state energy. This result covers the strong-coupling/low-density limit of the Lieb-Liniger model but applies to a much more general class of repulsive pair potentials, including potentials with a positive scattering length. A corresponding result follows straightforwardly for spinless fermions. Finally, we will conjecture an expansion of a similar structure for spin-1/2 fermions. The talk is based on joint work with Robin Reuvers and Jan Philip Solovej (arXiv:2203.17183) |
| 12:00-13:00 | Quantum Lunch. Speaker: Søren Fournais Title: Critical fields in Ginzburg-Landau theory in domains with corners Abstract: The spectral theory of Schr\”{o}dinger operators with magnetic fields on planar domains has seen a surge in activity in the last 10-20 years. In this talk I will overview some old results motivating the relation to the Ginzburg-Landau theory of superconductivity. Furthermore, I will present some recent progress and open problems. |
| 14:00-14:45 | Speaker: Lukas Lange Title: The energy of the 2D dilute Bose gas: an upper bound. Abstract: We provide an upper bound for the ground state energy density of the dilute Bose gase in the thermodynamical limit in two dimensions. We prove an expansion analogous to the famous Lee-Huang-Yang formula in 3D. Our result holds for essentially all the radial, positive potential with finite scattering length, in particular including the special case of the hard-core potential. From a joint work with S. Fournais, T. Girardot, L. Junge and L. Morin |
| 15:00-15:45 | Speaker: Marco Olivieri Title: A second order energy expansion for a dilute Bose gas in 2D: lower bound Abstract: We provide a lower bound for the ground state energy density of dilute Bose gases in the thermodynamical regime in two dimensions. We prove an expansion analogous to the famous Lee-Huang-Yang formula in 3D. Our result holds for essentially all the radial, positive potential with finite scattering length, in particular including the special case of the hard-core potential. We prove how the approximation to the second order can be reached by a refined combination of double localization techniques and renormalization of the potential. From a joint work with S. Fournais, T. Girardot, L. Junge and L. Morin. |