Related papers: Solving the Homogeneous Bethe-Salpeter Equation
In this paper, we consider the steady MHD equations with inhomogeneous boundary conditions for the velocity and the tangential component of the magnetic field. Using a new construction of the magnetic lifting, we obtain existence of weak…
Intertwining analysis, algebra, numerical analysis and optimization, computing conjugate co-gradients of real-valued quotients gives rise to eigenvalue problems. In the linear Hermitian case, by inspecting optimal quotients in terms of…
We have derived the Bethe-Salpeter (BS) equations for the collective-mode spectrum of a mixture of fermion atoms of two hyperfine states loaded into a moving optical lattice. The collective excitation spectrum exhibits rotonlike minimum and…
In this article we develop a high order accurate method to solve the incompressible boundary layer equations in a provably stable manner.~We first derive continuous energy estimates,~and then proceed to the discrete setting.~We formulate…
The Bethe-Salpeter Equation for a bound system, composed by two massive scalars exchanging a massive scalar, is quantitatively investigated in ladder approximation, within the Nakanishi integral representation approach. For the S-wave case,…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
By combining the algebraic Bethe ansatz and the off-diagonal Bethe ansatz, we investigate the supersymmetric t-J model with generic open boundaries. The eigenvalues of the transfer matrix are given in terms of an inhomogeneous T-Q relation,…
The Bethe-Salpeter equation for spin-one bottomonium coupled to quark and gluon propagators is solved in a class of non-trivial linear gauges. The interaction kernel is based on a known gluon propagator extrapolated from the lattice and…
We present an approach to solve a Bethe-Salpeter (BS) equation exactly without any approximation if the kernel of the BS equation exactly is instantaneous, and take positronium as an example to illustrate the general features of the…
The spinless Salpeter equation can be regarded as the eigenvalue equation of a Hamiltonian that involves the relativistic kinetic energy and therefore is, in general, a nonlocal operator. Accordingly, it is hard to find solutions of this…
We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct boundary data, we are provided with a large dataset of…
The four-point Green's function of static QED, where a fermion and an antifermion are located at fixed space positions, is calculated in covariant gauges. The bound state spectrum does not display any abnormal state corresponding to…
We have calculated the electromagnetic elastic form factor of a two body scalar bound state. The Bethe-Salpeter equation is solved directly in the Minkowski space using the Perturbation Theory Integral Representation. At soft coupling…
We study the rotations of a heavy string (helicoseir) about a vertical axis with one free endpoint and with arbitrary density, under the action of the gravitational force. We show that the problem can be transformed into a nonlinear…
The Bethe-Salpeter equation (BSE) for bound states in scalar theories is reformulated and solved in terms of a generalized spectral representation directly in Minkowski space. This differs from the conventional approach, where the BSE is…
The exact Bethe-Salpeter amplitude for the fermion-antifermion bound state in the Schwinger Model is investigated. The dependence on the relative time and position in the center-of-mass frame in all contributing instanton sectors is…
The scalar three-body Bethe-Salpeter equation, with zero-range interaction, is solved in Minkowski space by direct integration of the four-dimensional integral equation. The singularities appearing in the propagators are treated properly by…
We obtain the low-lying energy-momentum spectrum for the imaginary-time lattice four-Fermi or Gross-Neveu model in $d+1$ space-time dimensions ($d=1,2,3$) and with $N$-component fermions. Let $\kappa>0$ be the hopping parameter, $\lambda>0$…
We apply a new calculation scheme of a finite element method (FEM) for solving an elliptic boundary-value problem describing a quadrupole vibration collective nuclear model with tetrahedral symmetry. We use of shape functions constructed…
The Bethe ansatz in its several formulations is the common tool for the exact solution of one dimensional quantum Hamiltonians. This ansatz asserts that the several eigenfunctions of the Hamiltonians are given in terms of a sum of…