Douglas Lundholm: Lieb-Thirring bounds for interacting Bose gases

Abstract: The Lieb-Thirring inequality bounds the kinetic energy of a fermionic (i.e. antisymmetric) many-particle wave function in terms of its local particle density, and is an elegant and useful combination of the uncertainty and the exclusion principles of quantum mechanics. Such a bound was in work together with J. P. Solovej extended to more general identical particles, whose quantum statistics can be modeled using bosons with a local repulsive interaction, such as anyons in two dimensions, where Pauli repulsion is replaced by a local exclusion principle. Here we consider the generalization and application of similar energy bounds to a large family of pairwise interacting Bose gases, such as the hard-sphere gas in 3D, the hard-disk gas in 2D, as well as a general class of homogeneous potentials. This is recent joint work with F. Portmann and J. P. Solovej. I will also mention some work in progress together with F. Portmann and P. T. Nam.