Related papers: Spectral representation for on-shell massless doub…
The near threshold expansion of generalized sunset-type (water melon) diagrams with arbitrary masses is constructed by using a configuration space technique. We present analytical expressions for the expansion of the spectral density near…
We study the $\epsilon$-pseudospectra $\sigma_\epsilon(A)$ of square matrices $A \in \mathbb{C}^{N \times N}$. We give a complete characterization of the $\epsilon$-pseudospectrum of any $2 \times 2$ matrix and describe the asymptotic…
An expansion scheme is developed for Feynman diagrams describing the production of one massive and one massless particle near the threshold. As an example application, we compute the correlators of heavy-light quark currents, (\bar b…
We consider solutions of the massless scalar wave equation $\Box_g\psi=0$ on a fixed Rindler background and show polynomial decay of the energy flux related to the Rindler observers near null infinity and to local observers near the Rindler…
The particle production through the scalaron decays are considered for several different channels. The central part of the work is dedicated to a study of the decay probability into two complex minimally coupled massless scalars. The…
It is well-known that the convex and concave envelope of a multilinear polynomial over a box are polyhedral functions. Exponential-sized extended and projected formulations for these envelopes are also known. We consider the convexification…
The aim of this work is to analyze general infinite sums containing modified Bessel functions of the second kind. In particular we present a method for the construction of a proper asymptotic expansion for such series valid when one of the…
A numerical method is presented for first-principle simulations of charged colloidal dispersions in electrolyte solutions. Utilizing a smoothed profile for colloid-solvent boundaries, efficient mesoscopic simulations are enabled for…
Numerous tabletop experiments have been dedicated to exploring the manifestations of screened scalar field dark energy, such as symmetron or chameleon fields. Precise theoretical predictions require simulating field configurations within…
A deformed boson mapping of the Marumori type is derived for an underlying $su(2)$ algebra. As an example, we bosonize a pairing hamiltonian in a two level space, for which an exact treatment is possible. Comparisons are then made between…
The method of matched asymptotic expansions is applied to the problem of a collisionless plasma generated by UV illumination localized in a central part of the plasma in the limiting case of small Debye length ${\lambda}_D$. A…
In this paper, we briefly explain the spectral expansion problem for differential operators defined on the entire real line, generated by a differential expression with periodic, complex-valued coefficients.
A model of the thin shell expanding into a uniform ambient medium is developed. Density perturbations are described using equations with linear and quadratic terms, and the linear and the nonlinear solutions are compared. We follow the time…
Methods to detect the spectral sensitivity of an object using undulator radiation without monochromators or any other spectral devices are developed. The spectral transmission function of the object is calculated from its response to the…
We use the recently proposed generalised on-shell representation for scattering amplitudes and a consistency test to explore the space of tree-level consistent couplings in four-dimensional Minkowski spacetime. The extension of the…
Various procedures for expressing the multipolar expansion of the electromagnetic field are considered with application to the calculation of the radiated power. Some results from literature are discussed and perspective of developing the…
We use the on-shell S-matrix and form factors to compute anomalous dimensions of higher dimension operators in the Standard Model Effective Field Theory. We find that in many instances, these computations are made simple by using the…
We give a recursive formula for an expansion of a solution of a general non-autonomous polynomial differential equation. The formula is given on the algebraic level with a use of shuffle product. This approach minimizes the number of…
We explore the deep ultraviolet (that is, short-distance) limit of the power spectrum (PS) and of the correlation function of a cold dark matter dominated Universe. While for large scales the PS can be written as a double series expansion,…
We show that the method used in the Schwarzschild black hole for finding the elementary solution of the electrostatic equation in closed form cannot extend in higher dimensions. By contrast, we prove the existence of static, spherically…