Application of the gradient method to Hartree-Fock-Bogoliubov theory

A Numerical Perspective on Hartree-Fock-Bogoliubov Theory

The method of choice for describing attractive quantum systems is Hartree-Fock-Bogoliubov (HFB) theory. This is a nonlinear model which allows for the description of pairing effects, the main explanation for the superconductivity of certain materials at very low temperature. This paper is the first study of Hartree-Fock-Bogoliubov theory from the point of view of numerical analysis. We start by...

Symmetry-projected Hartree-Fock-Bogoliubov Equations

Symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations are derived using the variational ansatz for the generalized one-body density-matrix in the Valatin form. It is shown that the projected-energy functional can be completely expressed in terms of the HFB density-matrix and the pairing-tensor. The variation of this projected-energy is shown to result in HFB equations with modified express...

Hartree-Fock-Bogoliubov Calculations in the UCOM Framework

With the advent of new radioactive beam facilities like FAIR, the structure of exotic nuclei far beyond the valley of stability can be probed experimentally, providing a strong motivation for theoretical studies using ab initio approaches and interactions which provide a stringent link to QCD as the fundamental theory of the strong interaction. To this end, we apply second-generation VUCOM inte...

Contact Pairing Interaction for the Hartree- Fock-bogoliubov Calculations

Properties of density-dependent contact pairing interactions in nuclei are discussed. It is shown that the pairing interaction that is intermediate between surface and volume pairing forces gives the pairing gaps that are compatible with the experimental odd-even mass staggering. Results of the deformed Hartree-Fock-Bogoliubov calculations for this \mixed" pairing interaction, and using the tra...

Implicit ladder summation in the Hartree-Fock-Bogoliubov approach