Related papers: Sum rules for Confining Potentials
We present a new, highly efficient yet accurate approximation for the Green's functions of dressed particles, using the Holstein polaron as an example. Instead of summing a subclass of diagrams (e.g. the non-crossed ones, in the…
The spectral density of random matrices is studied through a quaternionic generalisation of the Green's function, which precisely describes the mean spectral density of a given matrix under a particular type of random perturbation. Exact…
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 perform a systematic study of $SU(2)$ flavor amplitude sum rules with particular emphasis on $U$-spin. This study reveals a rich mathematical structure underlying the sum rules that allows us to formulate an algorithm for deriving all…
A new technique based on H\"older's integral inequality is applied to QCD sum-rules to provide fundamental constraints on the sum-rule parameters. These constraints must be satisfied if the sum-rules are to consistently describe integrated…
We consider analytic functions of the Riemann zeta type, for which, if $s$ is a zero, so is $1-s$. We use infinite product representations of these functions, assuming their zeros to be of first order. We use exponential factors to…
We introduce an exactly solvable one-dimensional potential that supports both bound and/or resonance states. This potential is a generalization of the well-known 1D Morse potential where we introduced a deformation that preserves the finite…
A simple system of two particles in a bidimensional configurational space $S$ is studied. The possibility of breaking in $S$ the time independent Schr\"{o}dinger equation of the system into two separated one-dimensional one-body…
We prove limit theorems for sums of randomly chosen random variables conditioned on the summands. We consider several versions of the corner growth setting, including specific cases of dependence amongst the summands and summands with heavy…
Sum rules -- relating the static quark potential V(R) to the spatial distribution of the action and energy in the colour fields of flux-tubes -- are applied in three ways: 1) To extract generalised beta-functions: 2) As a consistency check…
Apparent inconsistencies between different formulations of nucleon sum rules at finite density are resolved through a proper accounting of asymmetries in the spectral functions between positive- and negative-energy states.
For the massless N=1supersymmetric electrodynamics, regularized by higher derivatives, the Feynman diagrams, which define the divergent part of the two-point Green function and can not be found from Schwinger-Dyson equations and Ward…
This is the third paper of a series revisiting the Faraday effect. The question of the absolute convergence of the sums over the band indices entering the Verdet constant is considered. In general, sum rules and traces per unit volume play…
We study the sum rules of the form $Z(s) = \sum_n E_n^{-s}$, where $E_n$ are the eigenvalues of the time--independent Schr\"odinger equation (in one or more dimensions) and $s$ is a rational number for which the series converges. We have…
We derive the first two moment sum rules of the conduction electron retarded self-energy for both the Falicov-Kimball model and the Hubbard model coupled to an external spatially uniform and time-dependent electric field (this derivation…
Bound states of the power-law and logarithmic potentials are calculated using a generalized pseudospectral method. The solution of the single-particle Schr\"odinger equation in a nonuniform and optimal spatial discretization offers accurate…
For a class of one-dimensional Schrodinger operators with polynomial potentials that includes Hermitian and PT-symmetric operators, we show that the zeros of scaled eigenfunctions have a limit disctibution in the complex plane as the…
Power series in which the summand satisfies a linear recurrence relation with polynomial coefficients are shown to be the solution of a linear differential or algebraic equation. Solving the associated differential or algebraic equation…
Motivated by current interest in quantum confinement potentials, especially with respect to the Stark spectroscopy of new types of quantum wells, we examine several novel one-dimensional singular oscillators. A Green function method is…
We introduce a shifted version of the binomial theorem, and use it to study some remarkable trigonometric integrals and their explicit rewriting in terms of binomial multiple sums. Motivated by the expressions of area generating functions…