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In this work, we extend the so-called typicality approach, originally formulated in statistical mechanics contexts, to $SU(2)$-invariant spin-network states. Our results do not depend on the physical interpretation of the spin network;…
We investigate the performance of fully convolutional networks to simulate the motion and interaction of surface waves in open and closed complex geometries. We focus on a U-Net architecture and analyse how well it generalises to geometric…
We derive the Gauss-Codazzi equation in the holonomy and plane-angle representations and we use the result to write a Gauss-Codazzi equation for a discrete (2+1)-dimensional manifold, triangulated by isosceles tetrahedra. This allows us to…
Cyclidic nets are introduced as discrete analogs of curvature line parametrized surfaces and orthogonal coordinate systems. A 2-dimensional cyclidic net is a piecewise smooth $C^1$-surface built from surface patches of Dupin cyclides, each…
Quantum information processing in the presence of continuous symmetry is of wide importance and exhibits many novel physical and mathematical phenomena. SU(d) is a continuous group of particular interest since it represents a fundamental…
We study theoretically the transfer of quantum information along bends in two-dimensional discrete lattices. Our analysis shows that the fidelity of the transfer decreases considerably, as a result of interactions in the neighbourhood of…
The notion of shifted quantum groups has recently played an important role in algebraic geometry. This subtle modification of the original definition brings more flexibility in the representation theory of quantum groups. The first part of…
We expand a set of notions recently introduced providing the general setting for a universal representation of the quantum structure on which quantum information stands. The dynamical evolution process associated with generic quantum…
We show that the path integral for the three-dimensional SU(2) BF theory with a Wilson loop or a spin network function inserted can be understood as the Rovelli-Smolin loop transform of a wavefunction in the Ashtekar connection…
The absence of global symmetries in a quantum gravity theory often requires the introduction of (new) symmetry-breaking defects, which appear as singular objects in the low-energy description. This has been formalized in the Cobordism…
We present a line of research aimed at investigating holographic dualities in the context of three dimensional quantum gravity within finite bounded regions. The bulk quantum geometrodynamics is provided by the Ponzano-Regge state-sum…
Considering the popularity of two-dimensional particle-in-cell simulations, a 2D model of plasma wakefield in the strongly nonlinear (bubble) regime in transversely non-uniform plasma is developed. A differential equation for the boundary…
We study 3d and 4d systems with a one-form global symmetry, explore their consequences, and analyze their gauging. For simplicity, we focus on $\mathbb{Z}_N$ one-form symmetries. A 3d topological quantum field theory (TQFT) $\mathcal{T}$…
The study of toy models in loop quantum gravity (LQG), defined as truncations of the full theory, is relevant to both the development of the LQG phenomenology, in cosmology and astrophysics, and the progress towards the resolution of the…
How does one generalize differential geometric constructs such as curvature of a manifold to the discrete world of graphs and other combinatorial structures? This problem carries significant importance for analyzing models of discrete…
We report the theoretical prediction and experimental observation of a new class of four-dimensional (4D) tensor singularities and their three-dimensional (3D) Euler-class descendants, protected by chiral and spacetime inversion symmetries…
We present a novel deep learning framework for flow field predictions in irregular domains when the solution is a function of the geometry of either the domain or objects inside the domain. Grid vertices in a computational fluid dynamics…
The space of states and operators for a large class of background independent theories of quantum spacetime dynamics is defined. The SU(2) spin networks of quantum general relativity are replaced by labelled compact two-dimensional…
Two-dimensional multi-layer materials with an induced moir\'e pattern, either due to strain or relative twist between layers, provide a versatile platform for exploring strongly correlated and topological electronic phenomena. While these…
The composite particle duality extends the notions of both flux attachment and statistical transmutation in spacetime dimensions beyond 2+1D. It constitutes an exact correspondence that can be understood either as a theoretical framework or…