Related papers: Topological spectrum of classical configurations
Topology forms a cornerstone in modern condensed matter and statistical physics, offering a new framework to classify the phases and phase transitions beyond the traditional Landau paradigm. However, it is widely believed that topological…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
We introduce a framework, twisted parametrized stable homotopy theory, for describing semi-infinite homotopy types. A twisted parametrized spectrum is a section of a bundle whose fibre is the category of spectra. We define these bundles in…
In these lecture notes we will try to give an introduction to the use of the mathematics of fibre bundles in the understanding of some global aspects of gauge theories, such as monopoles and instantons. They are primarily aimed at beginning…
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
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…
Topological states enable robust transport within disorder-rich media through integer invariants inextricably tied to the transmission of light, sound, or electrons. However, the challenge remains to exploit topological protection in a…
The musical realm is a promising area in which to expect to find nontrivial topological structures. This paper describes several kinds of metrics on musical data, and explores the implications of these metrics in two ways: via techniques of…
Continuum lattice grid structures which consist of joined elastic beams subject to flexural deformations are ubiquitous. In this work, we establish a theoretical framework of the topological dynamics of continuum lattice grid structures,…
The bulk band topology of symmetry invariant adiabatic systems in the thermodynamic limit are considered to be determined by the hopping energy. In this work, we present that in closed classical systems, due to generalized chiral symmetry…
The subject of topological defects has become a very attractive field of study given its apparent relevance to as diverse systems as the early universe and condensed matter. As usually envisaged the topology of the manifold M of the minima…
We introduce a geometric construction of a gauge field theory of a complex adaptive system. It is based on a suitable simplicial formulation of a discrete geometry that manifests relevant properties valid in the classical differentiable…
The equations for topological fields in the $4d$ higher spin theory are considered. It is shown that these fields contain a finite number of degrees of freedom that justifies their naming. The issue of construction of gauge invariant…
The force networks of different granular ensembles are defined and their topological properties studied using the tools of complex networks. In particular, for each set of grains compressed in a square box, it is introduced a force…
We study the topology associated with physical vector and scalar fields. A mathematical object, e.g., a ball, can be continuously deformed, without tearing or gluing, to make other topologically equivalent objects, e.g., a cube or a solid…
Topological phases of matter are one of the hallmarks of quantum condensed matter physics. One of their striking features is a bulk-boundary correspondence wherein the topological nature of the bulk manifests itself on boundaries via exotic…
Parametrized motion planning algorithms have high degree of flexibility and universality, they can work under a variety of external conditions, which are viewed as parameters and form part of the input of the algorithm. In this paper we…
We propose a topological characterization of Hamiltonians describing classical waves. Applying it to the magnetostatic surface spin waves that are important in spintronics applications, we settle the speculation over their topological…
The emergence of preferred classical variables within a many-body wavefunction is encoded in its entanglement structure in the form of redundant classical information shared between many spatially local subsystems. We show how such…