Schedule: Monday, April 28th, 14.00 - 16.00
Tuesday, April 29th, 10:00 - 12:00
Wednesday, April 30, 14:00 - 16:00
Monday, May 5th, 14:00 - 16:00
Wednesday, May 7th, 14:00 - 16:00
Aula Seminari (3rd floor)
Bd. 14 "Nave", Via Bonardi 9,
D-Mat Mathematics Department of PoliMi, Politecnico di Milano.
________________________________________________________________________
SPEAKER: Douglas Lundholm (Uppsala Universitet)
________________________________________________________________________
Mathematics of the 2D anyon gas
In the theory of quantum statistics, if one follows mathematical logic to its conclusion, one reaches the possibility of intermediate exchange statistics and “anyons”, i.e. identical particles different from bosons and fermions. Over the course of about 50 years this topic has evolved from merely an exotic possibility to an almost inevitability when orientation symmetry is broken, such as in effectively two-dimensional systems subject to rotation or an external magnetic field. The signature example is the fractional quantum Hall effect, and in just the last few years very strong signatures of individual anyons have finally arrived from experiments. However, the many-body theory necessary to study precise collective properties of anyons has remained rather undeveloped until relatively recently. This mini course will focus on the mathematics of the many-anyon gas, introduce some of the main concepts involved, and thus provide a foundation for further exploration of the topic, starting from the toy model of ideal anyons, to more realistic emergent models, and also promising applications to quantum computing.
Lecture plan:
I. Quantum statistics & transmutation
II. Local exclusion & stability
III. The almost-bosonic interacting anyon gas
IV. Emergent models: FQHE & polarons
V. Non-abelian anyons & topological quantum computing
Further information: https://sites.google.com/view/qmp25-intensiveperiod/courses
