Related papers: Solution of the Bethe Equation Through the Laplace…
We present a new method for solving the two-body Bethe-Salpeter equation in Minkowski space. It is based on the Nakanishi integral representation of the Bethe-Salpeter amplitude and on subsequent projection of the equation on the…
The problem of quasistatic and rate-independent evolution of elastic-plastic-brittle delamination at small strains is considered. Delamination processes for linear elastic bodies glued by an adhesive to each other or to a rigid outer…
In the paper we offer a functional-discrete method for solving the Cauchy problem for the first order ordinary differential equations (ODEs). This method (FD-method) is in some sense similar to the Adomian Decomposition Method. But it is…
A system of partial differential equations (PDEs) is derived to compute the full-field stress from an observed kinematic field when the flow rule governing the plastic deformation is unknown. These equations generalize previously proposed…
The present work proposes a well-balanced finite volume-type numerical method for the solution of non-conservative hyperbolic partial differential equations (PDEs) with source terms. The method is characterized, first, by the use of a…
The two-fermion bound system is an attractive subject of atomic and sub-atomic physics. Despite these systems are rather simple the study of two-particle bound states is challenging and still remains a source of progress in quantum theory.…
The high-precision solution of the radial Dirac equation is fundamental to relativistic quantum chemistry, essential for reliable pseudopotential generation and all-electron electronic structure methods. However, standard basis-set…
A recently proposed strongly correlated electron system associated with the Temperley-Lieb algebra is solved by means of the coordinate Bethe ansatz for periodic and closed boundary conditions.
We present a master equation describing the interaction of light with dielectric objects of arbitrary sizes and shapes. The quantum motion of the object, the quantum nature of light, as well as scattering processes to all orders in…
Recent developments of the covariant Bethe-Salpeter (BS) approach with the use of the separable interaction for the deuteron are reviewed. It is shown that the BS formalism allows a covariant description of various electromagnetic reactions…
The long-ranged nature of the Coulomb potential requires a proper accounting for the influence of even distant electrostatic boundaries in the determination of the solvation free energy of a charged solute. We introduce an exact rewriting…
We show that the {\it ab initio} calculations of nuclear thermodynamics can be performed efficiently using lattice effective field theory. The simulations use a new approach called the pinhole trace algorithm to calculate thermodynamic…
The Bethe-Salpeter amplitude is expanded on a hyperspherical basis, thereby reducing the original 4-dimensional integral equation into an infinite set of coupled 1-dimensional ones. It is shown that this representation offers a highly…
This is not a new result. Purpose of this work is to describe a method to search the analytical expression of the general real solution of the two-dimensional Laplace differential equation. This thing is not easy to find in scientific…
The primordial lithium problem remains a persistent motivation for new-physics modifications of Big Bang nucleosynthesis, yet the precision of the observed deuterium abundance now places strong constraints on such attempts. This indicates…
We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…
Three well-known solutions of the Gaudin equation are obtained under a set of standard assumptions. By relaxing one of these assumptions we introduce a class of mutually commuting Hamiltonians based on a different solution of the Gaudin…
{\bf Background:} Deuteron induced reactions are widely used to probe nuclear structure and astrophysical information. Those (d,p) reactions may be viewed as three-body reactions and described with Faddeev techniques. {\bf Purpose:} Faddeev…
Using the nested coordinate Bethe ansatz, we study 33-vertex models, where only one global charge with degenerate eigenvalues exists and each site possesses three internal degrees of freedom. In the context of Markovian processes, they…
The quantum $\tau_2$-model with generic site-dependent inhomogeneity and arbitrary boundary fields is studied via the off-diagonal Bethe Ansatz method. The eigenvalues of the corresponding transfer matrix are given in terms of an…