Related papers: Approximate, analytic solutions of the Bethe equat…
We consider an $N$-body system of charged particle coupled to gravitational, electromagnetic, and scalar fields. The metric on moduli space for the system can be considered if a relation among the charges and mass is satisfied, which…
The Bethe ansatz equations are presented for Bariev's correlated electron chain with boundaries. This is achieved by using the coordinate space Bethe ansatz method.
We apply the algebraic Bethe ansatz technique to the nuclear pairing problem with orbit dependent coupling constants and degenerate single particle energy levels. We find the exact energies and eigenstates. We show that for a given shell,…
The Bethe Ansatz is a method that is used in quantum integrable models in order to solve them explicitly. This method is explained here in a general framework, which applies to 1D quantum spin chains, 2D statistical lattice models (vertex…
The differential scattering cross section for the problem of charged ultrarelativistic particles motion near a flat beam of charged ultrarelativistic particles was obtained. The problem is considered in the eikonal approximation in the…
Analytical formulas for next-to-leading order temperature corrections to the thermal state variables of interacting nucleons in bulk matter are derived in the degenerate limit. The formalism developed is applicable to a wide class of…
The analytical treatment of the Greens function in the convergent close-coupling method [Bray et al. Comp. Phys. Comm. 203 147 (2016)] has been extended to charged targets. Furthermore, we show that this approach allows for calculation of…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
For the exactly solved reduced BCS model an electrostatic analogy exists; in particular it served to obtain the exact thermodynamic limit of the model from the Richardson Bethe ansatz equations. We present an electrostatic analogy for a…
Optimal control problem with a goal to squeeze wave packet of a trapped quantum particle is considered and solved analytically using adiabatic approximation. The analytical solution that drives the particle into a highly localized final…
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…
We propose an effective Bethe ansatz for solving quantum many-body systems near an integrable point. Our approach retains the functional form of the Bethe wave function while renormalizing the Bethe roots to account for…
We propose a new method to obtain approximate solutions for the Schr\"{o}dinger equation with an arbitrary potential that possesses bound states. This method, relying on the auxiliary field technique, allows in many cases to find analytical…
We define one-dimensional particles with generalized exchange statistics. The exact solution of a Hubbard-type Hamiltonian constructed with such particles is achieved using the Coordinate Bethe Ansatz. The chosen deformation of the…
A finite element discretization using a method of lines approached is proposed for approximately solving the Poisson-Nernst-Planck (PNP) equations. This discretization scheme enforces positivity of the computed solutions, corresponding to…
Alchemical transformations showed that perturbation theory can be applied also to changes in the atomic nuclear charges of a molecule. The alchemical path that connects two different chemical species involves the conceptualization of a…
A coupled two frequency Hill's equation is solved. Analytically approximate solution correct up-to first order is derived using modified Lindstedt Poincare perturbation method. For a wide range of controlling parameters we compare the…
Irreversible random sequential deposition of interacting particles is widely used to model aggregation phenomena in physical, chemical, and biophysical systems. We show that in one dimension the exact time dependent solution of such…
Starting from the general Lindhard theory describing the partition of particles energy in materials between ionisation and displacements, analytical approximate solutions have been derived, for media containing one and more atomic species,…
The asymmetric exclusion process on a ring in one-dimension is considered with a single defect particle. The steady state has previously been solved by a matrix product method. Here we use the Bethe ansatz to solve exactly for the long time…