PDE and applications: Novel approaches to the quantum many-body problem: matrix product state algorithms hybridized with mean-field techniques

  • Date: –11:15
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119 or Zoom: https://uu-se.zoom.us/j/67226102216
  • Lecturer: Adrian Kantian
  • Organiser: Matematiska institutionen
  • Contact person: Kaj Nyström
  • Seminarium

ABSTRACT: Obtaining quantitatively reliable results for systems of interacting quantum particles remains an enormous challenge in many current frontier areas of research, from the physics of solid state materials, to quantum matter at both high and low energies. In this presentation I will give an overview of recent progress made on this front, which enables efficient quantitative calculations for both the static as well as the dynamic non-equilibrium properties of the very broad class of quasi-one-dimensional systems of interacting quantum particles. This approach fuses so-called matrix-product-state based numerics (which finds an optimally compressed representation of the quantum many-body state) with techniques taken from static mean-field approaches. This results in a formalism with features of either a non-linear eigenvalue problem (in the static case) and of a non-linear PDE (in the dynamic case). I will illustrate the application of this approach, including its’ validation via alternate approaches, using models of ultra cold quantum matter, as it can be realised e.g. in experiments on ultra cold atomic atomic gasses.