Related papers: Strong-Coupling Extrapolation of Gell-Mann--Low Fu…
Soft extrapolation refers to the problem of recovering a function from its samples, multiplied by a fast-decaying window and perturbed by an additive noise, over an interval which is potentially larger than the essential support of the…
Variational weak-coupling perturbation theory yields converging approximations, uniformly in the coupling strength. This allows us to calculate directly the coefficients of `strong-coupling' expansions. For the anharmonic oscillator we…
We study the degree of reliability of extrapolation of complex electromagnetic permittivity functions based on their analyticity properties. Given two analytic functions, representing extrapolants of the same experimental data, we examine…
We compute asymptotic expansions for the negative eigenvalues of the Pauli operator in two dimensions perturbed by a weakly coupled potential with definite sign. Whereas previous results were limited to the case of radial magnetic fields…
We study a special class of four-point correlation functions of infinitely heavy half-BPS operators in planar N=4 SYM which admit factorization into a product of two octagon form factors. We demonstrate that these functions satisfy a system…
The feasibility of extrapolation of completely monotone functions can be quantified by examining the worst case scenario, whereby a pair of completely monotone functions agree on a given interval to a given relative precision, but differ as…
Weak-coupling expansions (conserving approximations) are carried out for the attractive Holstein and Hubbard models (on an infinite-dimensional hypercubic lattice) that include all bandstructure and vertex correction effects. Quantum…
The previous attempts of reconstructing the Gell-Mann-Low function \beta(g) of the \phi^4 theory by summing perturbation series give the asymptotic behavior \beta(g) = \beta_\infty g^\alpha in the limit g\to \infty, where \alpha \approx 1…
The Gell-Mann -- Low function \beta(g) in QED (g is the fine structure constant) is reconstructed. At large g, it behaves as \beta_\infty g^\alpha with \alpha\approx 1, \beta_\infty\approx 1.
We discuss the divergence problems recently identified in some extrapolation operators for weakly-relational numeric domains. We identify the cause of the divergences and point out that resorting to more concrete, syntactic domains can be…
We present a novel extrapolation scheme for high order series expansions. The idea is to express the series, obtained in orders of an external variable, in terms of an internal parameter of the system. Here we apply this method to the…
Different versions of the effective-range function method for charged particle collisions are studied and compared. In addition, a novel derivation of the standard effective-range function is presented from the analysis of Coulomb wave…
We derive bounds $ |\frac{d\psi(\alpha)}{d\alpha}| \leq 1 $, $ \frac{d(\frac{d\psi(\alpha)}{d\alpha}\psi(\alpha))}{d\alpha} \leq 1 $ on the GL (Gell-Mann--Low) function $\psi(\alpha)$ from the Kallen-Lehmann dispersion representation in…
A novel method of summation for power series is developed. The method is based on the self-similar approximation theory. The trick employed is in transforming, first, a series expansion into a product expansion and in applying the…
We study the 3-point functions of gauge-invariant scalar operators in four dimensional $\mathcal{N}=2$ superconformal quiver theories using supersymmetric localization in the planar limit of a large number of colors. By exploiting a web of…
The empirical copula process plays a central role in the asymptotic analysis of many statistical procedures which are based on copulas or ranks. Among other applications, results regarding its weak convergence can be used to develop…
Weak measurement is a new technique which allows one to describe the evolution of postselected quantum systems. It appears to be useful for resolving a variety of thorny quantum paradoxes, particularly when used to study properties of pairs…
The correlation function in quantum systems plays a vital role in decoding their properties and gaining insights into physical phenomena. Its interpretation corresponds to the propagation of particle excitations between space-time, similar…
In a weak measurement, the average output $\langle o\rangle$ of a probe that measures an observable $\hat{A}$ of a quantum system undergoing both a preparation in a state $\rho_i$ and a postselection in a state $E_\mathrm{f}$ is, to a good…
The method of self-similar root approximants has earlier been shown to provide accurate interpolating formulas for functions for which small-variable expansions are given and the behaviour of the functions at large variables is known. Now…