Related papers: Noncommutative properties of 0-hyperbolic graphs
Quantum hypergraph states are the natural generalization of graph states. Here we investigate and analytically quantify entanglement and nonlocality for large classes of quantum hypergraph states. More specifically, we connect the geometric…
The intention of the paper is to move a step towards a classification of network topologies that exhibit periodic quantum dynamics. We show that the evolution of a quantum system, whose hamiltonian is identical to the adjacency matrix of a…
We consider complex Henon maps which are quasi-hyperbolic. We show that a quasi-hyperbolic map is uniformly hyperbolic if and only if there are no tangencies between stable and unstable manifolds.
The symmetries of a finite graph are described by its automorphism group; in the setting of Woronowicz's quantum groups, a notion of a quantum automorphism group has been defined by Banica capturing the quantum symmetries of the graph. In…
Quantum graphity is a background independent model for emergent locality, spatial geometry and matter. The states of the system correspond to dynamical graphs on N vertices. At high energy, the graph describing the system is highly…
In this paper we prove that given a non-isotrivial family of hyperbolic curves in positive characteristic, the isomorphism type of the geometric fundamental group is not constant on the fibres of the family.
A chain of quantum subgroups of the quantum automorphism group of finite graphs has been introduced. It generalizes the construction of J. Bichon (see [3]) in a sense. A better bound of the non zero eigenvalues of the graph Laplacian has…
We follow up on previous work which found that commonly used graph evolution moves lead to conserved quantities that can be expressed in terms of the braiding of the graph in its embedding space. We study non-embedded graphs under three…
We give a cohomological characterization of Gromov relative hyperbolicity. As an application we prove a converse to the combination theorem for graphs of relatively hyperbolic groups given in a previous paper of the first author. We build…
In this article, we study quantum automorphism groups of distance-transitive graphs. We show that the odd graphs, the Hamming graphs $H(n,3)$, the Johnson graphs $J(n,2)$ and the Kneser graphs $K(n,2)$ do not have quantum symmetry. We also…
We examine a graph $\Gamma$ encoding the intersection of hyperplane carriers in a CAT(0) cube complex $\widetilde X$. The main result is that $\Gamma$ is quasi-isometric to a tree. This implies that a group $G$ acting properly and…
We prove that for every pair of quantum isomorphic graphs, their block trees and their block graphs are isomorphic, and that such an isomorphism can be chosen so that the corresponding blocks are quantum isomorphic -- in particular,…
This article is dedicated to the study of the acylindrical hyperbolicity of automorphism groups of graph products of groups. Our main result is that, if $\Gamma$ is a finite graph which contains at least two vertices and is not a join and…
Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph,…
This is a review of concepts of noncommutative supergeometry - namely Hilbert superspace, C*-superalgebra, quantum supergroup - and corresponding results. In particular, we present applications of noncommutative supergeometry in harmonic…
The "noncommutative graphs" which arise in quantum error correction are a special case of the quantum relations introduced in [N. Weaver, Quantum relations, Mem. Amer. Math. Soc. 215 (2012), v-vi, 81-140]. We use this perspective to…
Let $\Sigma$ be a hyperbolic surface. We study the set of curves on $\Sigma$ of a given type, i.e. in the mapping class group orbit of some fixed but otherwise arbitrary $\gamma_0$. For example, in the particular case that $\Sigma$ is a…
We look at isometric actions on arbitrary hyperbolic spaces of generalised Baumslag - Solitar groups of arbitrary dimension (the rank of the free abelian vertex and edge subgroups). It is known that being a hierarchically hyperbolic group…
Let k be a field. We show that all homogeneous noncommutative curves of genus zero over k are noncommutative P^1-bundles over a (possibly) noncommutative base. Using this result, we compute complete isomorphism invariants of homogeneous…
Two signed graphs are called switching isomorphic if one of them is isomorphic to a switching equivalent of the other. To determine the number of switching non-isomorphic signed graphs on a specific graph, we will establish a method based…