Related papers: Applications of intersection numbers in physics
Ordinary Coincidence Site Lattices (CSLs) are defined as the intersection of a lattice $\Gamma$ with a rotated copy $R\Gamma$ of itself. They are useful for classifying grain boundaries and have been studied extensively since the mid…
In the present review we provide an extensive analysis of the intertwinement between Feynman integrals and cohomology theories in the light of the recent developments. Feynman integrals enter in several perturbative methods for solving non…
The main goal of this article is to introduce new quantitative characteristics of cycles in finite simple connected graphs and to establish relations of these characteristics with the stretch and spanning tree congestion of graphs. The main…
In general graph theory, the only relationship between vertices are expressed via the edges. When the vertices are embedded in an Euclidean space, the geometric relationships between vertices and edges can be interesting objects of study.…
The review is a brief description of the state of problems in percolation theory and their numerous applications, which are analyzed on base of interesting papers published in the last 15-20 years. At the submitted papers are studied both…
We propose a new formula to compute Witten--Kontsevich intersection numbers. It is a closed formula, not involving recursion neither solving equations. It only involves sums over partitions of products of factorials, double factorials and…
Twisted links are a generalization of classical links and correspond to stably equivalence classes of links in thickened surfaces. In this paper we introduce twisted intersection colorings of a diagram and construct two invariants of a…
These lectures are intended to provide the theoretical basis of describing high-energy particle collisions at a level appropriate to graduate students in experimental high energy physics. They are supposed to be familiar with quantum…
This paper introduces an intersection theory problem for maps into a smooth manifold equipped with a stratification. We investigate the problem in the special case when the target is the unitary group and the domain is a circle. The first…
Studying the geometry of sets appearing in various problems of quantum information helps in understanding different parts of the theory. It is thus worthwhile to approach quantum mechanics from the angle of geometry -- this has already…
In this paper, a review on dielectric mixtures and the importance of the numerical simulations of dielectric mixtures are presented. It stresses on the interfacial polarization observed in mixtures. It is shown that this polarization can…
Recent experiments have used scattering to map the flow of electrons in a two-dimensional electron gas. Among other things, the data from these experiments show perseverance of regular interference fringes beyond the kinematic thermal…
This book is devoted to an informal discussion of patterns constructed for treating physical problems. Such patterns, when sufficiently formalized, are usually referred as "models", and tents to be applied not only in physics, but conquer…
We prove an intersection formula for two plane branches in terms of their semigroups and key polynomials. Then we provide a strong version of Bayer's theorem on the set of intersection numbers of two branches and apply it to the logarithmic…
Topology has appeared in different physical contexts. The most prominent application is topologically protected edge transport in condensed matter physics. The Chern number, the topological invariant of gapped Bloch Hamiltonians, is an…
Topologically ordered phase has emerged as one of most exciting concepts that not only broadens our understanding of phases of matter, but also has been found to have potential application in fault-tolerant quantum computation. The direct…
We expand correlation functions of the Langmann-Szabo-Zarembo (LSZ) model in terms of intersection numbers on the moduli space of complex curves. This provides an explicit, physically motivated example for the expansion of correlation…
We present an algorithmic method for analyzing networks of intersections with static signaling, with as primary example a line network that allows traffic flow over several intersections in one main direction. The method decomposes the…
We investigate the large intersection properties of the set of points that are approximated at a certain rate by a family of affine subspaces. We then apply our results to various sets arising in the metric theory of Diophantine…
A survey is given on mathematical structures which emerge in multi-loop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, specific iterated integrals. Both classes lead to sets of…