Related papers: Recurrence Formulas for Fully Exponentially Correl…
Through the following, we establish the conditions which allow us to express recursive sequences of real numbers, enumerated through the recurrence relation a_{n+1} = Aa_n + Ba_{n-1}, by means of algebraic equations in two variables of…
The description of the long-term dynamics of highly elliptic orbits under third-body perturbations may require an expansion of the disturbing function in series of the semi-major axes ratio up to higher orders. To avoid dealing with long…
The total energy and electron addition and removal spectra can in principle be obtained exactly from the one-body Green's function. In practice, the Green's function is obtained from an approximate self-energy. In the framework of many-body…
The Eynard-Orantin recursion formula provides an effective tool for certain enumeration problems in geometry. The formula requires a spectral curve and the recursion kernel. We present a uniform construction of the spectral curve and the…
We consider the recursion relation for loop integrands in planar N = 4 SYM generated by an all-line shift of momentum twistors. We examine the behaviour of the rational loop integrands when the shift parameter becomes large, and find that a…
We consider (3+1)-dimensional second-order evolutionary PDEs where the unknown $u$ enters only in the form of the 2nd-order partial derivatives. For such equations which possess a Lagrangian, we show that all of them have a symplectic…
Extreme mass-ratio inspirals (EMRIs) are expected to have considerable eccentricity when emitting gravitational waves (GWs) in the LISA band. Developing GW templates that remain phase accurate over these long inspirals requires the use of…
The calculation of realistic N-body wave functions for identical fermions is still an open problem in physics, chemistry, and materials science, even for N as small as two. A recently discovered fundamental algebraic structure of many-body…
A framework for developing new approximate electronic structure methods is presented, in which the correlation energy of a many-electron system in the ground state is computed as in the single-reference second-order many-body perturbation…
The short range repulsion between nucleons is treated by a unitary correlation operator which shifts the nucleons away from each other whenever their uncorrelated positions are within the replusive core. By formulating the correlation as a…
Multiple Mellin-Barnes integrals are often used for perturbative calculations in particle physics. In this context, the evaluation of such objects may be performed through residues calculations which lead to their expression as multiple…
Hypergeometric structures in single and multiscale Feynman integrals emerge in a wide class of topologies. Using integration-by-parts relations, associated master or scalar integrals have to be calculated. For this purpose it appears useful…
We develop a scheme to exactly evaluate the correlation energy in the random-phase approximation, based on linear response theory. It is demonstrated that our formula is completely equivalent to a contour integral representation recently…
A program RCFP will be presented for calculating standard quantities in the decomposition of many-electron matrix elements in atomic structure theory. The list of quantities wich are supported by the present program includes the…
We develop a recursive computational procedure to efficiently calculate the macroscopic dielectric function of multi-component metamaterials of arbitrary geometry and composition within the long wavelength approximation. Although the…
Loop calculations involve the evaluation of divergent integrals. Usually [1] one computes them in a number of dimensions different than four where the integral is convergent and then one performs the analytical continuation and considers…
We generalize the derivation of the Wallis formula for $\pi$ from a variational computation of the spectrum of the Hydrogen atom. We obtain infinite product formulas for certain combinations of gamma functions, which include irrational…
The frequency dependence of the self energy of a general many--body problem is identified as a main obstacle in correlation calculations based on local approaches. A frequency independent formulation is proposed instead and proven to yield…
We present a consistent \emph{ab initio} computation of the longitudinal response function $R_L$ in $^{40}$Ca using the coupled-cluster and Lorentz integral transform methods starting from chiral nucleon-nucleon and three-nucleon…
Some typical kinetic energy integrals which arise in the application of extended Hylleraas-configuration interaction (E-Hy-CI) function in the framework of Rayleigh-Ritz method of variation, have been evaluated analytically for two-electron…