Dr. Tobias Grass
Donostia International Physics Center, San Sebastián, Spain
Donostia International Physics Center, San Sebastián, Spain
Seminarium hybrydowe, sala Rady Dyscyplin (sala 16), 19.02.2026, 15:00
Title
Localization and condensation in fractal and hyperbolic lattices
Abstract
This talk explores how unconventional lattice connectivity—from self-similar fractals to negatively curved hyperbolic graphs—reshapes quantum phenomena on the single- and many-body level. Geometric tuning enables transport regimes ranging from sub-diffusive to localized, governed by the interplay of fractal dimension and level-spacing distributions. In bosonic systems, hyperbolic curvature allows 2D lattices to mimic the Bose-Einstein condensation of 3D cubic systems, whereas fractal structures suppress condensation and can trigger condensate fragmentation. These geometric effects extend to the strongly interacting regime, where the fractal dimensionality reflects in the boundaries of the Mott insulating phase.