Related papers: The no-defect conjecture in cosmic crystallography
The language and methods of algebraic topology, particularly homotopy theory, have been extensively used in the study of the identification, the classification and the evolution of defects. Topological methods provide the means for the…
The homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across a broad range of physical systems. Recently, experimental progress has been made in controlling and measuring colloidal inclusions…
We critically analyze the possibility of finding signatures of a phase transition by looking exclusively at static quantities of statistical systems, like e.g., the topology of potential energy sub-manifolds (PES). This topological…
Topological defects, in particular cosmic strings, give rise to an interesting mechanism for generating the primordial perturbations in the early Universe which are required to explain the present structure. An overview of the cosmic string…
Structure formation with topological defects is described. The main differences from inflationary models are highlighted. The results are compared with recent observations. It is concluded that all the defect models studied so far are in…
The distance conjecture diagnoses viable low-energy effective realisation of consistent theories of quantum gravity by examining their breakdown at infinite distance in their parameter space. At the same time, infinite distance points in…
On the basis of the principle that topological quantum phases arise from the scattering around space-time defects in higher dimensional unification, a geometric model is presented that associates with each quantum phase an element of a…
Clustering $\unicode{x2013}$ the tendency for neighbors of nodes to be connected $\unicode{x2013}$ quantifies the coupling of a complex network to its latent metric space. In random geometric graphs, clustering undergoes a continuous phase…
The space-like hypersurface of the Universe at the present cosmological time is a three-dimensional manifold. A non-trivial global topology of this space-like hypersurface would imply that the apparently observable universe (the sphere of…
This article gives the construction and complete classification of all three-dimensional spherical manifolds, and orders them by decreasing volume, in the context of multiconnected universe models with positive spatial curvature. It…
Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic…
Is the universe finite or infinite, and what shape does it have? These fundamental questions, of which relatively little is known, are typically studied within the context of the standard model of cosmology where the universe is assumed to…
Can the topology of a network that consists of many particles interacting with each other change in complexity when a phase transition occurs? The answer to this question is particularly interesting to understand the nature of phase…
We study the formation of topological defects in nonequilibrium phase transitions of both classical and quantum field theory. We examine three model systems. 1). The phase transition of a quantum scalar field in a FRW universe is analyzed…
When the density parameter is close to unity, the universe has a large curvature radius independently of its being hyperbolic, flat, or spherical. Whatever the curvature, the universe may have either a simply connected or a multiply…
Whether we live in a spatially finite universe, and what its shape and size may be, are among the fundamental long-standing questions in cosmology. These questions of topological nature have become particularly topical, given the wealth of…
Topological defects are found in a variety of systems, and their existence are robust under perturbations due to their topological nature. Here we introduce a new type of topological defects found in electromagnetic waves: topological spin…
Production of gravitational vacuum defects and their contribution to the energy density of our Universe are discussed. These topological microstructures (defects) could be produced in the result of creation of the Universe from "nothing"…
One of the ways that connectedness has been studied through the history of topology is by using chains, the so called chain connectedness. Here we combine this notion together with continuity up to a covering to provide the inheritance of…
Certain geometric properties of submanifolds of configuration space are numerically investigated for classical lattice phi^4 models in one and two dimensions. Peculiar behaviors of the computed geometric quantities are found only in the…