Related papers: Transiting topological sectors with the overlap
The problem of optimizing over random structures emerges in many areas of science and engineering, ranging from statistical physics to machine learning and artificial intelligence. For many such structures finding optimal solutions by means…
Consider the lattice of bounded linear operators on the space of Borel measures on a Polish space. We prove that the operators which are continuous with respect to the weak topology induced by the bounded measurable functions form a…
Momentum space topology of relativistic gauge theory is considered. The topological invariants in momentum space are introduced for the case, when there is the mass gap while the fermion Green functions admit zeros. The index theorem is…
A lattice gauge theory with an action polynomial in independent field variables is considered. The link variables are described by unconstrained complex matrices instead of unitary ones. A mechanism which permits to switch off in the…
We have initiated the study of topology of the space of coverings on grid domains. The space has the following constraint: while all the covering agents can move freely (we allow overlapping) on the domain, their union must cover the whole…
I introduce a novel mathematical framework integrating topological dynamics, operator algebras, and ergodic geometry to study lattices of asynchronous metric dynamical systems. Each node in the lattice carries an internal flow represented…
We establish several new relations between the discrete transition operator, the continuous Laplacian and the averaging operator associated with combinatorial and metric graphs. It is shown that these operators can be expressed through each…
For a particular lattice gauge theory with ${\mathbb Z}_2$ gauge invariance there is confinement for all couplings. The gauge fields, on lattice links, lie in the closed interval $[-1,1]$. It is proved that the expectation value of a…
Directional fields, including unit vector, line, and cross fields, are essential tools in the geometry processing toolkit. The topology of directional fields is characterized by their singularities. While singularities play an important…
I present the recent developments in a specific sub-field of chiral gauge theories on the lattice. This sub-field pertains to the use of infinitely many fermi fields to describe a single chiral field. In this approach, both anomalous and…
The purpose of this paper is to discuss the construction of a linear operator, referred to as the bubble transform, which maps scalar functions defined on a bounded domain $\Omega$ in $\mathbb{R}^n$ into a collection of functions with local…
An old and apparently persistent problem in numerical lattice QCD is that the simulations tend to get trapped in a sector of fixed topological charge when the lattice spacing is taken to zero. The effect sets in very rapidly and may…
Topologically ordered systems are characterized by topological invariants that are often calculated from the momentum space integration of a certain function that represents the curvature of the many-body state. The curvature function may…
The Fourier operator truncated on a finite symmetric interval is considered. The limiting behavior of its spectrum is discussed as the length of the interval tends to infinity.
We introduce the graph parameter readability and study it as a function of the number of vertices in a graph. Given a digraph D, an injective overlap labeling assigns a unique string to each vertex such that there is an arc from x to y if…
The application of Random Matrix Theory to the Dirac operator of QCD yields predictions for the probability distributions of the lowest eigenvalues. We measured Dirac operator spectra using massless overlap fermions in quenched QCD at…
Stochastic processes are commonly used models to describe dynamics of a wide variety of nonequilibrium phenomena ranging from electrical transport to biological motion. The transition matrix describing a stochastic process can be regarded…
We formulate a model of relativistic fermions moving in two Euclidean dimensions based on a tight-binding model of graphene. The eigenvalue spectrum of the resulting Dirac operator is solved numerically in smooth U(1) gauge field…
The overlap formula for the chiral determinant is presented and the realization of gauge anomalies and gauge field toplogy in this context is discussed. The ability of the overlap formalism to deal with supersymmetric theories and…
We analyze the eigenstates of a two-dimensional lattice with additional harmonic confinement in the presence of an artificial magnetic field. While the softness of the confinement makes a distinction between bulk and edge states difficult,…