Crystallography of hyperbolic lattices
Hyperbolic lattices are a revolutionary platform for tabletop simulations of holography and
quantum physics in curved space and facilitate efficient quantum error correcting codes …
quantum physics in curved space and facilitate efficient quantum error correcting codes …
Quantum simulation of hyperbolic space with circuit quantum electrodynamics: From graphs to geometry
We show how quantum many-body systems on hyperbolic lattices with nearest-neighbor
hopping and local interactions can be mapped onto quantum field theories in continuous …
hopping and local interactions can be mapped onto quantum field theories in continuous …
Line-graph lattices: Euclidean and non-Euclidean flat bands, and implementations in circuit quantum electrodynamics
Materials science and the study of the electronic properties of solids are a major field of
interest in both physics and engineering. The starting point for all such calculations is single …
interest in both physics and engineering. The starting point for all such calculations is single …
Density of states of tight-binding models in the hyperbolic plane
R Mosseri, J Vidal - Physical Review B, 2023 - APS
We study the energy spectrum of tight-binding Hamiltonians for regular hyperbolic tilings.
More specifically, we compute the density of states using the continued-fraction expansion of …
More specifically, we compute the density of states using the continued-fraction expansion of …
Unbounded Laplacians on graphs: basic spectral properties and the heat equation
Unbounded Laplacians on Graphs: Basic Spectral Properties and the Heat Equation
Introduction Page 1 Math. Model. Nat. Phenom. Vol. 5, No. 2, 2010, pp. 198-224 DOI …
Introduction Page 1 Math. Model. Nat. Phenom. Vol. 5, No. 2, 2010, pp. 198-224 DOI …
Cheeger inequalities for unbounded graph Laplacians
Cheeger inequalities for unbounded graph Laplacians Page 1 DOI 10.4171/JEMS/503 J. Eur.
Math. Soc. 17, 259–271 c European Mathematical Society 2015 Frank Bauer · Matthias Keller …
Math. Soc. 17, 259–271 c European Mathematical Society 2015 Frank Bauer · Matthias Keller …
A poset-based approach to curvature of hypergraphs
In this contribution, we represent hypergraphs as partially ordered sets or posets, and
provide a geometric framework based on posets to compute the Forman–Ricci curvature of …
provide a geometric framework based on posets to compute the Forman–Ricci curvature of …
[图书][B] Laplacians on infinite graphs
A Kostenko, N Nicolussi - 2023 - ems.press
The main focus in this memoir is on Laplacians on both weighted graphs and weighted
metric graphs. Let us emphasize that we consider infinite locally finite graphs and do not …
metric graphs. Let us emphasize that we consider infinite locally finite graphs and do not …
Curvature, geometry and spectral properties of planar graphs
M Keller - Discrete & Computational Geometry, 2011 - Springer
We introduce a curvature function for planar graphs to study the connection between the
curvature and the geometric and spectral properties of the graph. We show that non-positive …
curvature and the geometric and spectral properties of the graph. We show that non-positive …
Spectral radius of finite and infinite planar graphs and of graphs of bounded genus
It is well known that the spectral radius of a tree whose maximum degree is Δ cannot exceed
2Δ− 1. In this paper we derive similar bounds for arbitrary planar graphs and for graphs of …
2Δ− 1. In this paper we derive similar bounds for arbitrary planar graphs and for graphs of …