Related papers: Analytic Evaluation of Four-Particle Integrals wit…

In this work we present a novel strategy to evaluate multi-variable integrals with quantum circuits. The procedure first encodes the integration variables into a parametric circuit. The obtained circuit is then derived with respect to the…

Range-separated density-functional theory is an alternative approach to Kohn-Sham density-functional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into…

An improved method is presented for the numerical evaluation of multi-loop integrals in dimensional regularization. The technique is based on Mellin-Barnes representations, which have been used earlier to develop algorithms for the…

The recently proposed effective potential theory [Phys. Rev. Lett. 110, 235001 (2013)] allows evaluating transport in coupled plasmas with the well-developed formalisms for systems with binary collisions. To facilitate practical…

Many multi-loop calculations make use of integration by parts relations to reduce the large number of complicated Feynman integrals that arise in such calculations to a simpler basis of master integrals. Recently, Gluza, Kajda, and Kosower…

The phase-integral method (PIM) is an asymptotic method of the geometrical optics or semi-classical type for solving approximately, but in many cases very accurately, a wide class of differential equations in physics. Unlike the related…

Analytical methods are used to prove the existence of a periodic, symmetric solution with singularities in the planar 4-body problem. A numerical calculation and simulation are used to generate the orbit. The analytical method easily…

We discuss a progress in calculations of Feynman integrals based on the Gegenbauer Polynomial Technique and the Differential Equation Method. We demonstrate the results for a class of two-point two-loop diagrams and the evaluation of most…

An analytical-numeric calculation method of extremely complicated integrals is presented. These integrals appear often in magnet soliton theory. The appropriate analytical continuation and a corresponding integration contour allow to reduce…

This paper presents a joint optimisation framework for optimal estimation and stochastic optimal control with imperfect information. It provides a estimation and control scheme that can be decomposed into a classical optimal estimation step…

We have developed a field theory for strongly coupled Coulomb fluids, via introducing new functional--integral transformation of the electrostatic interaction energy. Our formalism not only reproduces the Lieb--Narnhofer lower bound, but…

We propose a numerical test of fundamental physics based on the complexity measure of a general set of functions, which is directly related to the Kolmogorov (or algorithmic) complexity studied in mathematics and computer science. The…

We develop an analytic approach to the four-point crossing equation in CFT, for general spacetime dimension. In a unitary CFT, the crossing equation (for, say, the s- and t-channel expansions) can be thought of as a vector equation in an…

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…

The Atomic Cluster Expansion (Drautz, Phys. Rev. B 99, 2019) provides a framework to systematically derive polynomial basis functions for approximating isometry and permutation invariant functions, particularly with an eye to modelling…

The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004) is generalized to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules.…

It is known that the variational methods are the most powerful tool for studying the Coulomb three-body bound state problem. However, they often suffer from loss of stability when the number of basis functions increases. This problem can be…

We consider the identifiability and stable numerical estimation of multiple parameters in a Cahn-Hilliard model for phase separation. Spatially resolved measurements of the phase fraction are assumed to be accessible, with which the…

A self-consistent many-body approach is proposed to build a first-principles crystal field theory, where crystal field parameters are calculated ab initio. Many-body theory is used to write the energy of the interacting system as a function…

The Coulomb gauge has at least two advantadges over other gauge choices in that bound states between quarks and studies of confinement are easier to understand in this gauge. However, perturbative calculations, namely Feynman loop…