Dr Tobias Grass
Donostia International Physics Centre, San Sebastián, Spain
Hybrid seminar, Disciplines Council Room (Room 16), 19 February 2026, 3 p.m.
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Title
Localisation and condensation in fractal and hyperbolic lattices
Localisation 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 localised, 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 is reflected in the boundaries of the Mott insulating phase.
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 localised, 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 is reflected in the boundaries of the Mott insulating phase.