Related papers: 3-Cocycles and the Operator Product Expansion
We address the computational spectral theory of Jacobi operators that are compact perturbations of the free Jacobi operator via the asymptotic properties of a connection coefficient matrix. In particular, for finite-rank perturbation we…
In this paper we study spectral properties of Jacobi operators. In particular, we prove two main results: (1) that perturbing the diagonal coefficients of Jacobi operator, in an appropriate sense, results in exponential localization, and…
We first present some identities involving the Pochhammer symbol (rising factorial). We also recall and present some new properties of the Jacobi polynomials. We use them to expand a general hypergeometric function in an orthogonal series…
In this paper, we first develop a notion of dominated splitting for $\mathbb M(2,\mathbb C)$-sequences and show it is a stable property under $\|\cdot \|_\infty$-perturbation. Then we show an energy parameter belongs to the spectrum of a…
Let $\Delta$ be the Jacobi Laplacian. We study the chaotic and hypercyclic behaviour of the strongly continuous semigroups of operators generated by perturbations of $\Delta$ with a multiple of the identity on $L^p$ spaces.
We present certain results on the direct and inverse spectral theory of the Jacobi operator with complex periodic coefficients. For instance, we show that any $N$-th degree polynomial whose leading coefficient is $(-1)^N$ is the Hill…
We formulate extensions of Wilking's Jacobi field splitting theorem to uniformly positive sectional curvature and also to positive and nonnegative intermediate Ricci curvatures.
In a recent paper a class of infinite Jacobi matrices with discrete character of spectra has been introduced. With each Jacobi matrix from this class an analytic function is associated, called the characteristic function, whose zero set…
We evaluate the three-loop corrections to the matching coefficient of the vector current between Quantum Chromodynamics (QCD) and non-relativistic QCD. The result is presented in the MSbar scheme where large perturbative corrections are…
Anomalous quark triangles with one axial and two vector currents are studied in special kinematics when one of the vector currents carries a soft momentum. According to the Adler-Bardeen theorem the anomalous longitudinal part of the…
We study how the addition of defects in an otherwise uniform Josehpson junction array modifies the critical current of the array, by numerically solving the system of coupled Josephson equations. Our results confirm the existence of two…
In the setting of distributions taking values in a $C^\ast$-algebra $\mathcal{B}$, we define generalized Jacobi parameters and study distributions they generate. These include numerous known examples and one new family, of…
We study fractal dimension properties of singular Jacobi operators. We prove quantitative lower spectral/quantum dynamical bounds for general operators with strong repetition properties and controlled singularities. For analytic…
We compute the critical Josephson current through a single-molecule junction. As a model for a molecule with a bistable conformational degree of freedom, we study an interacting single-level quantum dot coupled to a two-level system and…
We propose an alternative to Dirac quantization for a quadratic constrained system. We show that this solves the Jacobi identity violation problem occuring in the Dirac quantization case and yields a well defined Fock space. By requiring…
We establish conceptually important properties of the operator product expansion (OPE) in the context of perturbative, Euclidean $\varphi^{4}$-quantum field theory. First, we demonstrate, generalizing earlier results and techniques of…
Two-loop contributions to the anomalous correlation function <J_mu(x)J_nu(y)J_rho(z)> of three chiral currents are calculated by a method based on the conformal properties of massless field theories. The method was previously applied to…
We derive a number of local identities of arbitrary rank involving Jacobi elliptic functions and use them to obtain several new results. First, we present an alternative, simpler derivation of the cyclic identities discovered by us…
In this paper, we study off-shell currents built from the Jacobi identity of the kinematic numerators of $gg\to X$ with $X=ss,q\bar{q},gg$. We find that these currents can be schematically written in terms of three-point interaction Feynman…
The Narasimhan-Nori conjecture asks for a closed formula for the number of non-isomorphic principal polarizations of any given abelian variety. In this paper, we introduce a new algorithm that gives a lower bound on the number of…