PDE and Applications: Mathematical methods for uncertainty and exclusion in quantum mechanics

  • Date: –11:15
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
  • Lecturer: Douglas Lundholm
  • Organiser: Matematiska institutionen
  • Contact person: Kaj Nyström
  • Seminarium

The success of quantum mechanics over classical mechanics in explaining properties of matter such as the periodic table of the elements, stability against collapse, etc, rests on two fundamental principles: the uncertainty principle and the exclusion principle. In 1975 Elliott Lieb and Walter Thirring found a powerful functional inequality, the Lieb-Thirring inequality, which incorporates these two principles and was used to prove stability for "ordinary matter" which is subject to fermionic statistics and Pauli's exclusion principle. Recently this inequality has been extended to situations where only weaker forms of exclusion apply, such as for certain contact interactions. If there is time I will also discuss exotic forms of particle statistics possible in two dimensions, namely "anyons" and their exclusion properties.