Related papers: Non-Weyl Resonance Asymptotics for Quantum Graphs

For the description of observables and states of a quantum system, it may be convenient to use a canonical Weyl algebra of which only a subalgebra $\mathcal A$, with a non-trivial center $\mathcal Z$, describes observables, the other Weyl…

We study a quantum (non-commutative) representation of the affine Weyl group mainly of type $E_8^{(1)}$, where the representation is given by birational actions on two variables $x$, $y$ with $q$-commutation relations. Using the tau…

We study Weyl symmetry for non-relativistic conformal filed theories on curved spatial spaces, and calculate it's quantum anomaly. We show that there is no geometric anomaly, and the non-relativistic Weyl anomaly can appear only due to…

We examine current numerical relativity computations of gravitational waves, which typically determine the asymptotic waves at infinity by extrapolation from finite (small) radii. Using simulations of a black hole binary with accurate wave…

Recently, the tunable Weyl-semimetal bands and the associate topological phase transition have been successfully simulated in superconducting quantum circuits [X. Tan, \textit{et al.} Phys. Rev. Lett. {\bf 122}, 010501 (2019)]. Since the…

The Weyl-gauge ($A_0^a=0)$ QCD Hamiltonian is unitarily transformed to a representation in which it is expressed entirely in terms of gauge-invariant quark and gluon fields. In a subspace of gauge-invariant states we have constructed that…

Using topological band theory analysis we show that the nonsymmorphic symmetry operations in hexagonal lattices enforce Weyl points at the screw-invariant high-symmetry lines of the band structure. The corepresentation theory and…

For a compact Riemannian manifold, Weyl's law describes the asymptotic behavior of the counting function of the eigenvalues of the associated Laplace operator. In this paper we discuss Weyl's law in the context of automorphic forms. The…

Let $G$ be a group and let $S$ be an inverse-closed and identity-free generating set of $G$. The \emph{Cayley graph} $\Cay(G,S)$ has vertex-set $G$ and two vertices $u$ and $v$ are adjacent if and only if $uv^{-1}\in S$. Let $CAY_d(n)$ be…

The Weyl-gauge ($A_0^a=0)$ QCD Hamiltonian is unitarily transformed to a representation in which it is expressed entirely in terms of gauge-invariant quark and gluon fields. In a subspace of gauge-invariant states we have constructed that…

There is a close connection between various new phenomena in Weyl semimetals and the existence of linear band crossings in the single particle description. We show, by a full self-consistent mean-field calculation, how this picture is…

This paper is concerned with small parameter asymptotics of magnetic quantum systems. In addition to a semiclassical parameter \eps, the case of small coupling $\lambda$ to the magnetic vector potential naturally occurs in this context.…

We investigate the relation between the eigenvalues of the Laplacian with Kirchhoff vertex conditions on a finite metric graph and a corresponding Titchmarsh-Weyl function (a parameter-dependent Neumann-to-Dirichlet map). We give a complete…

The Staruszkiewicz quantum model of the long-range structure in electrodynamics is reviewed in the form of a Weyl algebra. This is followed by a personal view on the asymptotic structure of quantum electrodynamics.

We establish the asymptotic behaviour of $\mu(G(n,p))$, the number of unlabelled induced subgraphs in the binomial random graph $G(n,p)$, for almost the entire range of the probability parameter $p=p(n)\in[0,1]$. In particular, we show that…

We prove that the asymptotic distribution of resonances has a multilevel internal structure for the following classes of Hamiltonians H: Schr\"odinger operators with point interactions in $\mathbb{R}^3$, quantum graphs, and 1-D photonic…

We find the asymptotic number of connected graphs with $k$ vertices and $k-1+l$ edges when $k,l$ approach infinity, reproving a result of Bender, Canfield and McKay. We use the {\em probabilistic method}, analyzing breadth-first search on…

Let $G\subset \O(n)$ be a group of isometries acting on $n$-dimensional Euclidean space $\R^n$, and ${\bf{X}}$ a bounded domain in $\R^n$ which is transformed into itself under the action of G. Consider a symmetric, classical…

The electronic structure of a cubic $\mathcal{T}$-symmetric Weyl semimetal is analysed in the presence of atomic-sized vacancy defects. Isolated vacancies are shown to generate nodal bound states with $r^{{\scriptscriptstyle -2}}$…

In this paper we consider quasi-normal modes of test scalar and electromagnetic fields in the background of a non-Schwarzschild black hole in the Einstein-Weyl gravity. We find the dependence of the modes on the new parameter $p$, which is…