相关论文: Stability of Salpeter Solutions
We review some important topics related to the semirelativistic description of bound states by the spinless Salpeter equation: the special case of the Coulomb interaction, numerical approximation methods, and a way to avoid the problematic…
Open quantum systems evolving according to discrete-time dynamics are capable, unlike continuous-time counterparts, to converge to a stable equilibrium in finite time with zero error. We consider dissipative quantum circuits consisting of…
The method of solving the Bethe-Salpeter equation in Minkowski space, which we developed previously for spinless particles, is extended to a system of two fermions. The method is based on the Nakanishi integral representation of the…
Self-consistent Hartree-Fock approximation combined with solutions of the Bethe-Salpeter equation offers a powerful tool for studies of strong correlation effects arising in condensed matter models, nuclear physics, quantum field theories,…
We present a method to directly solving the Bethe-Salpeter equation in Minkowski space, both for bound and scattering states. It is based on a proper treatment of the singularities which appear in the kernel, propagators and Bethe-Salpeter…
We use quantum electrodynamics and the Bethe-Salpeter equation to calculate the bound state energies for a two-particle system comprised of a spin-0 and spin-1/2 particle. We generalize our treatment to include the finite size of the…
The interaction kernel in the Bethe-Salpeter equation for quark-antiquark bound states is derived newly from QCD in the case where the quark and the antiquark are of different flavors. The technique of the derivation is the usage of the…
We consider a model of quantum field theory with higher derivatives for a spinor field with quartic selfinteraction. With the help of the Bethe-Salpeter equation we study the problem of the two particle bound states in the "chain"…
A quantum particle moving under the influence of singular interactions on embedded surfaces furnish an interesting example from the spectral point of view. In these problems, the possible occurrence of a bound state is perhaps the most…
The asymptotic behaviour of the Hartree equation is studied near translation-invariant steady states. For short-range interaction kernels satisfying a uniform Penrose stability condition, including the screened Coulomb interaction,…
The study of asymptotic properties of solutions to differential equations has a long and arduous history, with the most significant advances having been made in the development of quantum mechanics. A very powerful method of analysis is…
We use an alternative method to the Bethe-Salpeter equation, the N-Quantum approximation (NQA), for studying bound states in motion. We use this method to find a relativistic equation for weakly bound states of two constituents with…
We investigate the stability of the wave equation with spatial dependent coefficients on a bounded multidimensional domain. The system is stabilized via a scattering passive feedback law. We formulate the wave equation in a port-Hamiltonian…
A two-particle self-consistency is rarely part of mean-field theories. It is, however, essential for avoiding spurious critical transitions and unphysical behavior. We present a general scheme for constructing analytically controllable…
In this contribution, I will give a brief survey of present techniques to treat the bound state problem in relativistic quantum field theories. In particular, I will discuss the Bethe-Salpeter equation, various quasi-potential equations,…
We analyze the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process on a finite lattice and with the most general open boundary conditions. We extend results obtained…
This paper deals with the homogeneous Neumann boundary-value problem for the Keller--Segel system \begin{align*} \begin{cases} u_t=\Delta u - \chi \nabla \cdot (u|\nabla v|^{p-2}\nabla v),\\[] v_t=\Delta v - v + u^{\theta} \end{cases}…
We investigate entropy minimization problems for quantum states subject to convex block-separable constraints. Our principal result is a quantitative stability theorem: under a natural confining (fixed-support) hypothesis, if a state has…
The generalized pseudospectral Legendre method is used to carry out accurate calculations of eigenvalues of the spherically confined isotropic harmonic oscillator with impenetrable boundaries. The energy of the confined state is found to be…
We show that the only solutions of the TAP equations for the Sherrington-Kirkpatrick model of Ising spin glasses which can be found by iteration are those whose free energy lies on the border between replica symmetric and broken replica…