Related papers: O(4) Expansion of the ladder Bethe-Salpeter equati…
Isolated patches of spatially oscillating pattern have been found to emerge near a pattern-forming instability in a wide variety of experiments and mathematical models. However, there is currently no mathematical theory to explain this…
We choose a complete set of square integrable functions as basis for the expansion of the wavefunction in configuration space such that the matrix representation of the nonrelativistic time-independent wave operator is tridiagonal and…
We use variable transformation from the real line to finite or semi-infinite spaces where we expand the regular solution of the 1D time-independent Schrodinger equation in terms of square integrable bases. We also require that the basis…
For the first time, the inhomogeneous Bethe-Salpeter Equation for an interacting system, composed by two massive scalars exchanging a massive scalar, is numerically investigated in ladder approximation, directly in Minkowski space, by using…
A new solvable hyperbolic single wave potential is found by expanding the regular solution of the 1D Schr\"odinger equation in terms of square integrable basis. The main characteristic of the basis is in supporting an infinite tridiagonal…
The Harper equation describes an electron on a 2D lattice in magnetic field and a particle on a 1D lattice in a periodic potential, in general, incommensurate with the lattice potential. We find the distribution of the roots of Bethe ansatz…
In quantum theory, bound states are described by eigenvalue equations, which usually cannot be solved exactly. However, some simple general theorems allow to derive rigorous statements about the corresponding solutions, that is, energy…
We derive the so-called Barbieri-Remiddi solution of the Bethe-Salpeter equation in QED in its general form and discuss its application to the bound state energy spectrum.
The one-dimensional harmonic vibronic model, which is a generalization of the so-called linear Landau-Zener model and appears in the form of coupled Schr\"{o}dinger equations, is revisited. After decoupling the components, the resulting…
Among hyperbolic Initial Boundary Value Problems (IBVP), those coming from a variational principle 'generically' admit linear surface waves, as was shown by Serre [J. Funct. Anal. 2006]. At the weakly nonlinear level, the behavior of…
We study the large time behavior of solutions to the wave equation with space-dependent damping in an exterior domain. We show that if the damping is effective, then the solution is asymptotically expanded in terms of solutions of…
For the coefficients of the amplitude a set of simultaneous equations is derived in momentum space. By the auxiliary conditions they are equivalent to nonrelativistic equations and suitable for the investigation of two-nucleon system.
Analytical complexity of quantum wavefunction whose argument is extended into the complex plane provides an important information about the potentiality of manifesting complex quantum dynamics such as time-irreversibility, dissipation and…
We compare two opposite ways of performing a 3D reduction of the two-fermion Bethe-Salpeter equation beyond the instantaneous approximation and Salpeter's equation. The more usual method consists in performing an expansion around an…
We consider rotating wave solutions of the nonlinear wave equation \[ \left\{ \begin{aligned} \partial_{t}^2 v - \Delta v + m v & = |v|^{p-2} v \quad && \text{in $\mathbb{R} \times \textbf{B}$} \\ v & = 0 && \text{on $\mathbb{R} \times…
The nested algebraic Bethe ansatz is presented for the anisotropic supersymmetric $U$ model maintaining quantum supersymmetry. The Bethe ansatz equations of the model are obtained on a one-dimensional closed lattice and an expression for…
By application of the 'geometric spectral inversion' technique, which we have recently generalized to accommodate also singular interaction potentials, we construct from spectral data emerging from the solution of the Minkowski-space…
We consider the spectrum of the totally asymmetric simple exclusion process on a periodic lattice of $L$ sites. The first eigenstates have an eigenvalue with real part scaling as $L^{-3/2}$ for large $L$ with finite density of particles.…
The homogeneous Bethe-Salpeter equation (hBSE), describing a bound system in a genuinely relativistic quantum-field theory framework, was solved for the first time by using a D-Wave quantum annealer. After applying standard techniques of…
Consequent application of the instantaneous approximation to both the interaction and all propagators of the bound-state constituents allows us to forge, within the framework of the Bethe-Salpeter formalism for the description of bound…