The mass of simple and higher-order networks
arXiv:2309.07851 · doi:10.1088/1751-8121/ad0fb5
Abstract
We propose a theoretical framework that explains how the mass of simple and higher-order networks emerges from their topology and geometry. We use the discrete topological Dirac operator to define an action for a massless self-interacting topological Dirac field inspired by the Nambu-Jona Lasinio model. The mass of the network is strictly speaking the mass of this topological Dirac field defined on the network; it results from the chiral symmetry breaking of the model and satisfies a self-consistent gap equation. Interestingly, it is shown that the mass of a network depends on its spectral properties, topology, and geometry. Due to the breaking of the matter-antimatter symmetry observed for the harmonic modes of the discrete topological Dirac operator, two possible definitions of the network mass can be given. For both possible definitions, the mass of the network comes from a gap equation with the difference among the two definitions encoded in the value of the bare mass. Indeed, the bare mass can be determined either by the Betti number or by the Betti number of the network. We provide numerical results on the mass of different networks, including random graphs, scale-free, and real weighted collaboration networks. We also discuss the generalization of these results to higher-order networks, defining the mass of simplicial complexes. The observed dependence of the mass of the considered topological Dirac field with the topology and geometry of the network could lead to interesting physics in the scenario in which the considered Dirac field is coupled with a dynamical evolution of the underlying network structure.
arXiv comment(25 pages, 4 figures)
References in corpus (56)
- Emergence of scaling in random networks
- QCD Phenomenology based on a Chiral Effective Lagrangian
- The physics of higher-order interactions in complex systems
- Bose-Einstein condensation in complex networks
- Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation
- Simulating Lattice Gauge Theories within Quantum Technologies
- Emergence of a 4D World from Causal Quantum Gravity
- Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics
- Lattice gauge theories and string dynamics in Rydberg atom quantum simulators
- Lattice gauge theories simulations in the quantum information era
- Spin Network States in Gauge Theory
- Inhomogeneous chiral condensates
- Matter matters in asymptotically safe quantum gravity
- Artificial gauge fields in materials and engineered systems
- Identifying modular flows on multilayer networks reveals highly overlapping organization in social systems
- Quantum Graphity: a model of emergent locality
- Fractal properties of quantum spacetime
- Spectral entropies as information-theoretic tools for complex network comparison
- Emergent Hyperbolic Network Geometry
- Network geometry with flavor: from complexity to quantum geometry
- The Shannon and the Von Neumann entropy of random networks with heterogeneous expected degree
- Complex Networks from Classical to Quantum
- Classification of Finite Spectral Triples
- Emergent Complex Network Geometry
- Probing the quantum nature of spacetime by diffusion
- Spectral Statistics for the Dirac Operator on Graphs
- Weighted simplicial complexes and their representation power of higher-order network data and topology
- Reconfigurable optical implementation of quantum complex networks
- Complex quantum networks as structured environments: engineering and probing
- Dirac and magnetic Schrödinger operators on fractals
- Combinatorial Quantum Gravity: Geometry from Random Bits
- The topological Dirac equation of networks and simplicial complexes
- Inhomogeneous charged pion condensation in chiral asymmetric dense quark matter in the framework of NJL model
- Quantum Gravity as an Information Network: Self-Organization of a 4D Universe
- Persistent Dirac for molecular representation
- Charged pion condensation and duality in dense and hot chirally and isospin asymmetric quark matter in the framework of NJL model
- Dirac signal processing of higher-order topological signals
- The spin contribution to the form factor of quantum graphs
- Laplacians on discrete and quantum geometries
- Dirac synchronization is rhythmic and explosive
- Sign problems, noise, and chiral symmetry breaking in a QCD-like theory
- Phase structure of the 1+1 dimensional Nambu--Jona-Lasinio model with isospin
- Diffusion-driven instability of topological signals coupled by the Dirac operator
- The higher-order spectrum of simplicial complexes: a renormalization group approach
- Local Dirac Synchronization on Networks
- Dirac gauge theory for topological spinors in 3+1 dimensional networks
- Statistical mechanics of graph models and their implications for emergent spacetime manifolds
- Solitary waves in the Nonlinear Dirac Equation
- Dirac Operators and the Calculation of the Connes Metric on arbitrary (Infinite) Graphs
- Graph Laplacians, Riemannian Manifolds and their Machine-Learning
- Solitary Waves in a Discrete Nonlinear Dirac equation
- The birth of geometry in exponential random graphs
- Spectral and scattering theory for Gauss-Bonnet operators on perturbed topological crystals
- Physics in non-fixed spatial dimensions via random networks
- Emergent spacetime from purely random structures
- A sprinkling of hybrid-signature discrete spacetimes in real-world networks