Related papers: On the analytic solution of the pairing problem: o…
Nuclear pairing is studied both in atomic nuclei and in neutron-star crusts in the unified framework of the energy-density functional theory using generalized Skyrme functionals complemented with a local pairing functional obtained from…
The ground state of a general pairing Hamiltonian for a finite nuclear system is constructed as a product of collective, real, distinct pairs. These are determined sequentially via an iterative variational procedure that resorts to…
Real numbers provide a sufficient description of classical physics and all measurable phenomena; however, complex numbers are occasionally utilized as a convenient mathematical tool to aid our calculations. On the other hand, the formalism…
We give the exact solution of orbit dependent nuclear pairing problem between two non-degenerate energy levels using the Bethe ansatz technique. Our solution reduces to previously solved cases in the appropriate limits including…
The fundamental structure of the full set of solutions of the BCS $^3 P_2$ pairing problem in neutron matter is established. The relations between different spin-angle components in these solutions are shown to be practically independent of…
Low-lying energy levels of two interacting electrons confined in a two-dimensional parabolic quantum dot in the presence of an external magnetic field have been revised within the frame of a novel model. The present formalism, which gives…
We obtain a representation of pairing energies in phase space, for the Lipkin-Meshkov-Glick and general boson Bardeen-Cooper-Schrieffer pairing models. This is done by means of a probability distribution of the quantum state in phase space.…
The full theoretical analysis of the kinetics of multicomponent nucleation is presented. The relief of the free energy with surface excesses was analyzed, the valleys and ridges were described, their mutual interaction was studied. The new…
Richardson approach provides an exact solution of the pairing Hamiltonian. This Hamiltonian is characterized by the electron-hole pairing symmetry, which is however hidden in Richardson equations. By analyzing this symmetry and using an…
For quantum systems with competing potentials, the conventional perturbation theory often yields an asymptotic series and the subsequent numerical outcome becomes uncertain. To tackle such kind of problems, we develop a general solution…
Accurate solution of the many-electron problem including correlations remains intractable except for few-electron systems. Describing interacting electrons as a superposition of independent electron configurations results in an apparent…
A chart for the quantum mechanics of a particle of mass $m$ in a one-dimensional potential well of width $w$ and depth $V_0$ is derived. The chart is obtained by normalizing energy and potential through multiplication by ${8 m}{w^2} / h^2$,…
Pairing correlations in symmetric nuclear matter are studied within a relativistic mean-field approximation based on a field theory of nucleons coupled to neutral ($\sigma$ and $\omega$) and to charged ($\varrho$) mesons. The Hartree-Fock…
Analytic solutions of the quantum relativistic two-body problem are obtained for an interaction potential modeled as a one-dimensional smooth square well. Both stationary and moving pairs are considered and the limit of the…
In this paper a review is given of a class of sub-models of both approaches, characterized by the fact that they can be solved exactly, highlighting in the process a number of generic results related to both the nature of pair-correlated…
There is recent interest in the inter and intra element interactions of metamaterial unit cells. To calculate the effects of these interactions which can be substantial, an ab initio general coupled mode equation, in the form of an…
We present a method to obtain soliton solutions to relativistic system of coupled scalar fields. This is done by examining the energy associated to static field configurations. In this case we derive a set of first-order differential…
We use a combination of perturbation theory and numerical techniques to study the equilibration of two interacting fields which are initially at thermal equilibrium at different temperatures. Using standard rules of quantum field theory, we…
We derive the approximate solution for the pairing Hamiltonian in the Berggren ensemble of single particle states including bound, resonance and non-resonant scattering states. We show that this solution is reliable in the limit of a weak…
We obtain an exact solution of the 1D Dirac equation for a square well potential of depth greater then twice the particle's mass. The energy spectrum formula in the Klein zone is surprisingly very simple and independent of the depth of the…