Ана Кнежевић

08. новембра 2023.

У оквиру семинара Групе за гравитацију, честице и поља Института за физику у Београду, у петак, 10. новембра 2023. године у 11 часова у сали 360, Ана Кнежевић (Физички факултет Универзитета у Београду) одржаће предавање:

Hyperbolic lattices


Hyperbolic lattices connect gravitational theories, topology, algebraic geometry, condensed matter physics, etc. They are a new form of synthetic quantum matter, where particles propagate coherently on the sites of a regular structure that appears aperiodic from the vantage point of Euclidean geometry but is periodic in the case of 2D hyperbolic space. The lattice that we are researching is embedded in the Poincaré disk. We will start by comparing lattices in 2D Euclidean geometry with those in 2D hyperbolic space. In order to put any {p,q} (Schläfli symbols) lattice on a Poincaré disk, we will go back to our hyperbolic space and analyze its symmetry.  Our main goal is to construct discrete symmetry of the {p,q}-lattice from the Lié algebra (continual symmetry) of the hyperbolic space. In this manner, we can describe the hyperbolic crystal on the same footing as a crystalline lattice in flat space, which will furthermore allow us to systematically study band structures on such curved-space crystals.

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