Related papers: Use of Topology in physical problems
Euclidean geometry has historically played a central role in cultivating logical reasoning and abstract thinking within mathematics education, but has experienced waning emphasis in recent curricula. The resurgence of interest, driven by…
The notion of a coherent space is a nonlinear version of the notion of a complex Euclidean space: The vector space axioms are dropped while the notion of inner product is kept. Coherent spaces provide a setting for the study of geometry in…
Recent discoveries have demonstrated that matter can be distinguished on the basis of topological considerations, giving rise to the concept of topological phase. Introduced originally in condensed matter physics, the physics of topological…
A fundamental characteristic of computer networks is their topological structure. The question of the description of the structural characteristics of computer networks represents a problem that is not completely solved. Search methods for…
Data science offers a powerful tool to understand objects in multiple sciences. In this paper we utilize concept of data science, most notably topological data analysis, to extend our understanding of knot theory. This approach provides a…
These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.
Topological photonics is emerging as a new paradigm for the development of both classical and quantum photonic architectures. What makes topological photonics remarkably intriguing is the built-in protection as well as intrinsic…
In this work, we explore the state-space formulation of network processes to recover the underlying structure of the network (local connections). To do so, we employ subspace techniques borrowed from system identification literature and…
We study necessary conditions on the geometry and the topology of domains in $\mathbb{R}^2$ that support a positive solution to a classical overdetermined elliptic problem. The ideas and tools we use come from constant mean curvature…
Universe structure emerges in the unreduced, complex-dynamical interaction process with the simplest initial configuration (two attracting homogeneous fields). The unreduced interaction analysis avoiding any perturbative model gives…
Few physical systems with topologies more complicated than simple gaussian linking have been explored in detail. Here we focus on examples with higher topologies in non-relativistic quantum mechanics and in QCD.
Topology, a well-established concept in mathematics, has nowadays become essential to describe condensed matter. At its core are chiral electron states on the bulk, surfaces and edges of the condensed matter systems, in which spin and…
Current theories of particle physics lead to the unavoidable conclusion that there must have been several phase transitions in the early universe. Further, in the context of these theories, it is possible that cosmological phase transitions…
General relativity is unable to determine the topology of the Universe. We propose to apply quantum approach. Quantization of dynamics of a test particle is sensitive to the spacetime topology. Presented results for a particle in de Sitter…
Knot theory provides a powerful tool for the understanding of topological matters in biology, chemistry, and physics. Here knot theory is introduced to describe topological phases in the quantum spin system. Exactly solvable models with…
Toposes can be pictured as mathematical universes. Besides the standard topos, in which most of mathematics unfolds, there is a colorful host of alternate toposes in which mathematics plays out slightly differently. For instance, there are…
In this article we give the basic concept of the "Topological Numbers" in theory of quasiperiodic functions. The main attention is paid to apperance of such values in transport phenomena including Galvanomagnetic phenomena in normal metals…
Topological defects (TDs) are crucial for understanding important physical properties of crystalline materials including mechanical failure, ion transport, and two-dimensional melting. This concept has not translated to disordered materials…
The research effort reported in this paper is directed, in a broad sense, towards understanding the small-scale structure of spacetime. The fundamental question that guides our discussion is ``what is the physical content of spacetime…
The global topology of the Universe could, in principle, affect quantum systems through boundary condition constraints. We investigate this connection by analyzing how compact, flat, cosmologically inspired topologies, specifically the…