Related papers: Topological Properties of Spatial Coherence Functi…
Coherent states have three main properties: coherence, overcompleteness and intrinsic geometrization. These unique properties play fundamental roles in field theory, especially, in the description of classical domains and quantum…
A salient feature of topological phases are surface states and many of the widely studied physical properties are directly tied to their existence. Although less explored, a variety of topological phases can however similarly be…
We study the persistent homology of both functional data on compact topological spaces and structural data presented as compact metric measure spaces. One of our goals is to define persistent homology so as to capture primarily properties…
We study geometric and topological properties of locally compact, geodesically complete spaces with an upper curvature bound. We control the size of singular subsets, discuss homotopical and measure-theoretic stratifications and regularity…
In this paper we analyze some relationships between the topological complexity of a space $X$ and the category of $C_{\Delta_X},$ the homotopy cofibre of the diagonal map $\Delta_X:X\rightarrow X\times X.$ We establish the equality of the…
We develop an analytical formalism to determine the statistical properties of a system consisting of an ensemble of vortices with random position in plane interacting with a turbulent field. We calculate the generating functional by…
We consider periodic quantum Hamiltonians on the torus phase space (Harper-like Hamiltonians). We calculate the topological Chern index which characterizes each spectral band in the generic case. This calculation is made by a semi-classical…
We extend the wide-sense spatial stationarity concept of coherence holography in the regime of phase-space using the wigner distribution function. We focus mainly on the incoherent light source and the Fourier and Fresnel propagation…
We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of…
The paper is devoted to the study of homotopy properties of stabilizers of smooth functions on oriented surfaces, i.e., groups of diffeomorphisms of surfaces preserving a given function. For some class of smooth functions which is a…
Coherence properties are central to quantum systems and are at the heart of phenomena such as superconductivity. Here we study coherence properties of an ultracold Bose gas in a two-dimensional optical lattice across the thermal phase…
We combine Homotopy Type Theory with axiomatic cohesion, expressing the latter internally with a version of "adjoint logic" in which the discretization and codiscretization modalities are characterized using a judgmental formalism of "crisp…
We study the homology of free loop spaces via techniques arising from the theory of topological coHochschild homology (coTHH). Topological coHochschild homology is a topological analogue of the classical theory of coHochschild homology for…
We study iterated function systems (IFS) with compact parameter space. We show that the space of IFS with phase space $X$ is the hyperspace of the space of self continuous maps of $X$. With this result we obtain that the Hausdorff distance…
In this paper we introduce congruence spaces, which are topological spaces that are canonically attached to monoid schemes and that reflect closed topological properties. This leads to satisfactory topological characterizations of closed…
There are several topological spaces associated to a complex hyperplane arrangement: the complement and its boundary manifold, as well as the Milnor fiber and its own boundary. All these spaces are related in various ways, primarily by a…
Multiple harmonic sums appear in the perturbative computation of various quantities of interest in quantum field theory. In this article we introduce a class of Hopf algebras that describe the structure of such sums, and develop some of…
In this paper, we generalize the concept of unicoherence to the context of frames. Unicoherence, originally introduced by Kuratowski, is a connectedness property that is well studied in classical topology and used to detect holes of a…
We study certain integer valued length functions on triangulated categories and establish a correspondence between such functions and cohomological functors taking values in the category of finite length modules over some ring. The…
The topological phase acquired by vector vortex optical beams is investigated. Under local unitary operations on their polarization and transverse degrees of freedom, the vector vortices can only acquire discrete geometric phase values, 0…