Related papers: Asymptotics of classical spin networks

Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by…

We construct a generating functional for the exact evalutation of a coherent representation of spin network amplitudes. This generating functional is defined for arbitrary graphs and depends only on a pair of spinors for each edge. The…

The SU(2) Wigner function represents a quantum state of a spin-$J$ as a real-valued function on the surface of a 2-sphere. For an ensemble of $N$ spin-1/2 particles, this representation is useful when the dynamics is restricted to a single…

In this paper, we discuss different models for human logic systems and describe a game with nature. G\"odel`s incompleteness theorem is taken into account to construct a model of logical networks based on axioms obtained by symmetry…

Gauge theories on graphs and networks are attracting increasing attention not only as approaches to quantum gravity but also as models for performing quantum computation. Here we propose a Dirac gauge theory for topological spinors in $3+1$…

Automata networks can be seen as bare finite dynamical systems, but their growing theory has shown the importance of the underlying communication graph of such networks. This paper tackles the question of what dynamics can be realized up to…

We present an asymptotic formula for the number of line segments connecting q+1 points of an nxn square grid, and a sharper formula, assuming the Riemann hypothesis. We also present asymptotic formulas for the number of lines through at…

For a simple model of shallow and wide neural networks, we show that the epigraph of its input-output map as a function of the network parameters approximates epigraph of a. convex function in a precise sense. This leads to a plausible…

We study a general model of random dynamical simplicial complexes and derive a formula for the asymptotic degree distribution. This asymptotic formula encompasses results for a number of existing models, including random Apollonian networks…

We study the formation and evolution of an interconnected string network in large-scale field-theory numerical simulations, both in flat spacetime and in expanding universe. The network consists of gauge U(1) strings of two different kinds…

We study behaviour of trajectories near a type Z heteroclinic network which is a union of two cycles. Analytical and numerical studies indicate that attractiveness of this network can be associated with various kinds of dynamics in its…

An embedded cubic graph consisting of segments of geodesics such that the angles at any vertex are equal to $2\pi/3$ is a closed local minimal net. This net is regular if all segments of geodesics are equal. The problem of classification of…

Symmetry is a fundamentally important concept in many branches of physics. In this work, we discuss two types of symmetries, external symmetry and internal symmetry, which appear frequently in controlled quantum spin chains and apply them…

In a network of spin 1/2 particles, controlled through an external electro-magnetic field, the gyromagnetic ratio of each spin is a parameter that characterizes the interaction of the spin with the external control field. Multipartite…

A string-net model associates a vector space to a surface in terms of graphs decorated by objects and morphisms of a pivotal fusion category modulo local relations. String-net models are usually considered for spherical fusion categories,…

We propose an approach to formulating string theory in a curved spacetime, which is based on the connection between the states of the WZW model for the isometry group of a background spacetime metric and the representations of the…

Superbubbles are acyclic induced subgraphs of a digraph with single entrance and exit that naturally arise in the context of genome assembly and the analysis of genome alignments in computational biology. These structures can be computed in…

Quantum chaotic systems exhibit certain universal statistical properties that closely resemble predictions from random matrix theory (RMT). With respect to observables, it has recently been conjectured that, when truncated to a sufficiently…

As a toy model for the microscopic description of matter in de Sitter space, we consider a Hamiltonian acting on the spin-j representation of SU(2). This is a model with a finite-dimensional Hilbert space, from which quasinormal modes…

Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…