The Ising model describes a many-body interacting spin (or particle) system, which can be utilized to imitate the fundamental forces of nature. Although it is the simplest many-body interacting system of spins (or particles) with Z2 symmetry, the phe...
Topological field theories (TFTs) have captured the attention of mathematicians due to their various applications. In categorical terms, an nTFT is defined as a monoidal functor that maps the category of n-dimensional cobordisms to the category of ve...
An alternative to conventional spacetime is proposed and rigorously formulated for nonlocal continuum field theories through the deployment of a fiber bundle-based superspace extension method. We develop, in increasing complexity, the concept of nonl...
The Maxwell-BF theory with a single-sided planar boundary is considered in Euclidean four-dimensional spacetime. The presence of a boundary breaks the Ward identities, which describe the gauge symmetries of the theory, and, using standard methods of...
I review a new superconductivity mechanism in which the gap is opened through a topological mechanism and not through the Landau mechanism of spontaneous symmetry breaking. As a consequence, the low-energy effective theory which describes these new s...
The mathematical universe of the quantum topos, which is formulated on the basis of classical Boolean snapshots, delivers a neo-realist description of quantum mechanics that preserves realism. The main contribution of this article is developing forma...
The classical thermostatics of equilibrium processes is shown to possess a quantum mechanical dual theory with a finite dimensional Hilbert space of quantum states. Specifically, the kernel of a certain Hamiltonian operator becomes the Hilbert space of...
Spatially uniform optical excitations can induce Floquet topological band structures within insulators which can develop similar or equal characteristics as are known from three-dimensional topological insulators. We derive in this article theoretica...
Relativistic heavy ion collisions represent an arena for the probe of various anomalous transport effects. Those effects, in turn, reveal the correspondence between the solid state physics and the high energy physics, which share the common formalism...
Stagnation graphs provide a useful tool to analyze the main topological features of the often complicated vector field associated with magnetically induced currents. Previously, these graphs have been constructed using response quantities appropriate...
Quantum mechanics postulates wave–particle duality and assigns amplitudes of the form eiS/ℏ, yet no existing formulation explains why physical observables depend only on the phase of the action. Here we show that if the quantum of action...
In this paper, we consider the topological abelian BF theory with radial boundary on a generic 3D manifold, as we were motivated by the recently discovered accelerated edge modes on certain Hall systems. Our aim was to research if, where, and how the...
The definition of a length operator in quantum cosmology is usually influenced by a quantum theory for gravity considered. The semiclassical limit at the Planck age must meet the requirements implied in present observations. The features of a semicla...
We review the topological gauge theory description of Josephson junction arrays (JJA), fabricated systems which exhibit the superconductor-to-insulator transition (SIT). This description revealed the topological nature of the phases around the SIT an...
We survey the recent developments on quantum invariants of 3-manifolds and links: Z^ and FL. They are q-series invariants originated from mathematical physics, inspired by the categorification of a numerical quantum invariant—the Witten–R...
We find that the whole set of known baryons of spin parity JP=12+ (the ground state) and JP=32+ (the first excited state) is organized in multiplets which may efficiently be encoded by the multiplets of conjugacy classes in the small finite group G=(...
Topological fluctuations change their nature in the different phases of strong interactions, and the interrelation of topology, chiral symmetry and confinement at high temperature has been investigated in many lattice studies. This review is devoted...
In this paper, we study operator reconstruction in a class of holographic tensor networks describing renormalization group flows studied in arXiv:2210.12127. We study examples of 2D bulk holographic tensor networks constructed from Dijkgraaf–Wi...
The second, lower-temperature nematic phase observed in nonlinear dimer liquid crystals has properties originating from nanoscale, polar, intermolecular packing preferences. It fits the description of a new liquid crystal phase discovered by Vanakara...
Ferroelectric materials, characterized by spontaneous electric polarization, exhibit remarkable parallels with fluid dynamics, where polarization flux behaves similarly to fluid flow. Understanding polarization distribution in confined geometries at...
We study the connection between quantum and topological entanglement. We present several of the simplest examples of topological systems that can simulate quantum entanglement. We also propose to use toric cobordisms as a code space for a quantum com...
Homology groups are a prime tool for measuring the connectivity of a network, and their computation in a distributed and adaptive way is mandatory for their use in sensor networks. In this paper, we propose a solution based on the construction of an...
In this paper, we discuss various aspects of a class of A-twisted heterotic Landau–Ginzburg models on a Kähler variety X. We provide a classification of the R-symmetries in these models which allow the A-twist to be implemented, focusing o...
Topological susceptibility of the SU(3) gluon plasma is calculated by accounting for both factorized and non-factorized contributions to the two-point correlation function of topological-charge densities. It turns out that, while the factorized contr...
The present paper deals with two types of topologies on the set of integers, Z : a quasi-discrete topology and a topology satisfying the T 1 2 -separation axiom. Furthermore, for each n ∈ N , we develop countably many topologies...
We review the recent progress in the study of line defects in three-dimensional Chern–Simons-matter superconformal field theories, notably the ABJM theory. The first part is focused on kinematical defects, supporting a topological sector of the theor...
At every point p on a smooth n-manifold M there exist n+1 skew-symmetric tensor spaces spanning differential r-forms ω with r=0,1,⋯,n. Because d∘d is always zero where d is the exterior differential, it follows that every exact r-fo...
The field of mathematics that studies the relationship between algebraic structures and graphs is known as algebraic graph theory. It incorporates concepts from graph theory, which examines the characteristics and topology of graphs, with those from...
Mountain mudslides have emerged as one of the main geological dangers in the Yanshan region of China as a result of excessive rains. In light of this, a multi-step debris flow hazard assessment method combining optimal weights and a topological objec...
In the field of data science and data mining, the problem associated with clustering features and determining its optimum number is still under research consideration. This paper presents a new 2D clustering algorithm based on a mathematical topologi...
This paper falls under the heading of constructing consistent self-couplings in topological BF models. Our endeavor is of interest in the context of pure gravity, General Relativity, and super-gravity in Ashtekar formalism, which allow for certain ec...
Three-dimensional topological insulators possess surface-conducting states in the bulk energy gap, which are topologically protected and can be well described as helical 2 + 1 Dirac fermions. The electromagnetic response is given by axion electrodyna...
Topology optimization is a powerful structural design method that determines the optimal configuration by distributing materials efficiently within a given design domain while satisfying specified load, performance, and volume constraints. Unlike siz...
Symmetry (and group theory) is a fundamental principle of theoretical physics. Finite symmetries, continuous symmetries of compact groups, and infinite-dimensional representations of noncompact Lie groups are at the core of solid physics, particle ph...
As a layered topological nodal line semimetals hosting a quasi-one-dimensional (quasi-1D) crystalline structure, TaNiTe5 has attracted intensive attention. In this research, we analyze the low temperature (low-T) transport properties in single crysta...
It has been found that the topology effect and the possible emergent hidden scale and hidden local flavor symmetries at high density reveal a novel structure of compact star matter. When Nf≥2, baryons can be described by skyrmions when the number...
In this paper, we provide a brief introduction to the main notions of geometric group theory and of asymptotic topology of finitely generated groups. We will start by presenting the basis of discrete groups and of the topology at infinity, then we wi...
The main purpose of this paper is to show and introduce some new interpretative aspects of the concept of “emergent space” as geometric/topological approach in the cosmological field. We will present some possible applications of this theory, among w...
The realization of a BRST cohomology of the 4D topological gauge-affine gravity is established in terms of a superconnection formalism. The identification of fields in the quantized theory occurs directly as is usual in terms of superconnection and i...
Graph theory has much great advances in the field of mathematical chemistry. Chemical graph theory has become very popular among researchers because of its wide applications in mathematical chemistry. The molecular topological descriptors are the num...
Complex network science is an interdisciplinary field of study based on graph theory, statistical mechanics, and data science. With the powerful tools now available in complex network theory for the study of network topology, it is obvious that compl...
We prove various results in infinite-dimensional differential calculus that relate the differentiability properties of functions and associated operator-valued functions (e.g., differentials). The results are applied in two areas: (1) in the theory o...
In the present paper, we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution structure...
A topological constraint, characterized by the Casimir invariant, imparts non-trivial structures in a complex system. We construct a kinetic theory in a constrained phase space (infinite-dimensional function space of macroscopic fields), and characte...
Transformation optics enables engineering of the effective topology and dimensionality of the optical space in metamaterials. Nonlinear optics of such metamaterials may mimic Kaluza-Klein theories having one or more kinds of effective charges. As a r...
The 4D Maxwell theory with single-sided planar boundary is considered. As a consequence of the presence of the boundary, two broken Ward identities are recovered, which, on-shell, give rise to two conserved currents living on the edge. A Kaç-M...
Lattice formulations of gravity can be used to study non-perturbative aspects of quantum gravity. Causal Dynamical Triangulations (CDT) is a lattice model of gravity that has been used in this way. It has a built-in time foliation but is coordinate-i...
In the low-energy regime, baryons with Nf≥2 have long been constructed as skyrmions or through bag models, but such constructions for Nf=1 are hindered by the trivial topological structure of the meson field. Recent proposals suggest that one-flav...
First-principles calculations of the electronic ground state in tantalum arsenide are combined with tight-binding calculations of the field dependence of its transport model equivalent on the graphene monolayer to study the emergence of topologically...
Graph theory can be used to optimize interconnection network systems. The compatibility of such networks mainly depends on their topology. Topological indices may characterize the topology of such networks. In this work, we studied a symmetric networ...
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