Related papers: Solving the Homogeneous Bethe-Salpeter Equation
We present a high-performance solver for dense skew-symmetric matrix eigenvalue problems. Our work is motivated by applications in computational quantum physics, where one solution approach to solve the so-called Bethe-Salpeter equation…
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…
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…
The $e^-$-$e^+$ bound state spectrum of QED3 is investigated in the quenched ladder approximation to the homogeneous Bethe-Salpeter equation with fermion propagators from a rainbow approximation Schwinger-Dyson equation. A detailed analysis…
A relativistic two-body wave equation, local in configuration space, is derived from the Bethe-Salpeter equation for two scalar particles bound by a scalar Coulomb interaction. The two-body bound-state wave equation is solved analytically,…
We use the Bethe Ansatz solution for the one dimensional Hubbard model with open boundary conditions and applied boundary fields to study the spectrum of bound states at the boundary. Depending on the strength of the boundary potentials one…
In this paper, we used some theorems of fixed point for studying the results of Existence and Uniqueness For Hilfer-Hadamard-Type Fractional Differential Equations, \[_{H}D^{\alpha,\beta}x(t)+f(t,x(t))=0, ~~~~~~ on~~the~~ interval~~…
Considering a spin-up and a spin-down fermion in a generic tight-binding lattice with a multi-site basis, we investigate the two-body problem using a multiband extended-Hubbard model with finite-ranged hopping and interaction parameters. We…
A one-dimensional Bose Hubbard model with unidirectional hopping is shown to be exactly solvable. Applying the algebraic Bethe ansatz method, we prove the integrability of the model and derive the Bethe ansatz equations. The exact…
The problem of the fictitious frequency spectrum resulting from numerical implementations of the boundary element method for the exterior Helmholtz problem is revisited. When the ordinary 3D free space Green's function is replaced by a…
The algebraic Bethe Ansatz is a prosperous and well-established method for solving one-dimensional quantum models exactly. The solution of the complex eigenvalue problem is thereby reduced to the solution of a set of algebraic equations.…
The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to PDEs without the need of a fundamental solution. A theoretical framework for the convergence…
Observing renewed interest in long-standing (semi-) relativistic descriptions of bound states, we would like to make a few comments on the eigenvalue problem posed by the spinless Salpeter equation and, illustrated by the examples of the…
The bound state problem for a fermion-antifermion system is considered taking into account a finite decay width of the constituents. We propose an exactly solvable relativistic zero order equation similar to that of Barbieri and Remiddi,…
The Bethe-Salpeter equation and leptonic decay constants for pseudoscalar and vector quark-antiquark mesons with arbitrary quark masses are studied in Coulomb gauge, under a leading order truncation. As input, we use a pure linear rising…
A homogenization approach is one of effective strategies to solve multiscale elliptic problems approximately. The finite element heterogeneous multiscale method (FEHMM) which is based on the finite element makes possible to simulate such…
We present the Minkowski space solutions of the inhomogeneous Bethe-Salpeter equation for spinless particles with a ladder kernel. The off-mass shell scattering amplitude is first obtained.
The reduction of the two fermion Bethe-Salpeter equation in the framework of light-front dynamics is studied for one gauge A+=0. The arising effective interaction can be perturbatively expanded in powers of the coupling constant g, allowing…
The Nested Bethe Ansatz is generalized to open boundary conditions. This is used to find the exact eigenvectors and eigenvalues of the $A_{n-1}$ vertex model with fixed open boundary conditions and the corresponding $SU_{q}(n)$ invariant…
We study the rate of convergence for (variational) eigenvalues of several non-linear problems involving oscillating weights and subject to different kinds of boundary conditions in bounded domains.