Douglas Lundholm: Lieb-Thirring inequalities for intermediate and fractional statistics

Abstract: Standard quantum mechanics predicts two types of identical particles in nature: bosons (such as photons) and fermions (such as electrons). However, in one and two spatial dimensions there is a logical possibility for identical quantum particles different from bosons and fermions, obeying intermediate or fractional (anyon) statistics. I will review recent extensions of a family of useful bounds for the energy of a many-particle wave function in terms of its density, the Lieb-Thirring inequalities, to models of anyons in two dimensions, as well as to models in one dimension of Lieb-Liniger and Calogero-Sutherland type. This is joint work with Jan Philip Solovej. Some very recent generalizations are also joint with Fabian Portmann.