Related papers: Asymptotics of classical spin networks

The semiclassical mechanics of the Wigner 6j-symbol is examined from the standpoint of WKB theory for multidimensional, integrable systems, to explore the geometrical issues surrounding the Ponzano-Regge formula. The relations among the…

In this paper Moussouris' algorithm for the decomposition of spin networks is reviewed and the implicit assumptions made in the Decomposition Theorem relating a spin network with its state sum are examined. It is found that the theorem in…

We introduce gauge networks as generalizations of spin networks and lattice gauge fields to almost-commutative manifolds. The configuration space of quiver representations (modulo equivalence) in the category of finite spectral triples is…

Asymptotic properties of random regular graphs are object of extensive study in mathematics. In this note we argue, based on theory of spin glasses, that in random regular graphs the maximum cut size asymptotically equals the number of…

A gauge invariant Hamiltonian representation for SU(2) in terms of a spin network basis is introduced. The vectors of the spin network basis are independent and the electric part of the Hamiltonian is diagonal in this representation. The…

This paper treats 6j symbols or their orthonormal forms as a function of two variables spanning a square manifold which we call the "screen". We show that this approach gives important and interesting insight. This two dimensional…

Spin networks in Loop Quantum Gravity are traditionally described by unitary holonomies corresponding to noiseless transformations. In this work, we extend this framework to incorporate general quantum channels that model effects of…

The 10j symbol is a spin network that appears in the partition function for the Barrett-Crane model of Riemannian quantum gravity. Elementary methods of calculating the 10j symbol require order(j^9) or more operations and order(j^2) or more…

I discuss the role played by the spin-network basis and recoupling theory (in its graphical tangle-theoretic formulation) and their use for performing explicit calculations in loop quantum gravity. In particular, I show that recoupling…

Relativistic spin networks are defined by considering the spin covering of the group SO(4), SU(2) times SU(2). Relativistic quantum spins are related to the geometry of the 2-dimensional faces of a 4-simplex. This extends the idea of…

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;…

Quantum network is a set of nodes connected with channels, through which the nodes communicate photons and classical information. Classical structural complexity of a quantum network may be defined through its physical structure, i.e.…

In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…

In this article initial steps in an analysis of cyclic networks of quantum logic gates is given. Cyclic networks are those in which the qubit lines are loops. Here we have studied one and two qubit systems plus two qubit cyclic systems…

Projected spin network states are the canonical basis of quantum states of geometry for the most recent EPR-FK spinfoam models for quantum gravity. They are functionals of both the Lorentz connection and the time normal field. We analyze in…

A spin nematic is a state which breaks spin SU(2) symmetry while preserving translational and time reversal symmetries. Spin nematic order can arise naturally from charge fluctuations of a spin stripe state. Focusing on the possible…

The algebraic consistency of spin and isospin at the level of an unbroken SU(2) gauge theory suggests the existence of an additional angular momentum besides the spin and isospin and also produces a full quaternionic spinor operator. The…

We construct a new discrete basis of 4-valent SU(2) intertwiners. This basis possesses both the advantage of being discrete, while at the same time representing accurately the classical degrees of freedom; hence it is coherent. The closed…

We describe an example of a structurally stable heteroclinic network for which nearby orbits exhibit irregular but sustained switching between the various sub-cycles in the network. The mechanism for switching is the presence of spiralling…

Neural networks are one of the most popularly used methods in machine learning and artificial intelligence nowadays. Due to the universal approximation theorem (Hornik et al. (1989)), a neural network with one hidden layer can approximate…