$\frac{{\rm SO}(2N)}{U(N)}$ Riccati–Hartree–Bogoliubov equation based on the SO(2N) Lie algebra of the fermion operators

In this paper we present the induced representation of SO (2N) canonical transformation group and introduce [Formula: see text] coset variables. We give a derivation of the time-dependent Hartree–Bogoliubov (TDHB) equation on the Kähler coset space [Formula: see text] from the Euler–Lagrange equation of motion for the coset variables. The TDHB wave function represents the TD behavior of Bose condensate of fermion pairs. It is a good approximation for the ground state of the fermion system with a pairing interaction, producing the spontaneous Bose condensation. To describe the classical motion on the coset manifold, we start from the local equation of motion. This equation becomes a Riccati-type equation. After giving a simple two-level model and a solution for a coset variable, we can get successfully a general solution of time-dependent Riccati–Hartree–Bogoliubov equation for the coset variables. We obtain the Harish-Chandra decomposition for the SO (2N) matrix based on the nonlinear Möbius transformation together with the geodesic flow on the manifold.

PAIRING VIBRATIONS STUDY FROM TIME-DEPENDENT HARTREE-FOCK-BOGOLIUBOV FORMALISM

We study pairing vibrations in 18,20,22 O and 42,44,46 Ca nuclei solving the time-dependent Hartree-Fock-Bogoliubov equation in coordinate space with spherical symmetry. We use the SLy4 Skyrme functional in the particle-hole part of the energy density functional and a local, density-dependent pairing functional in its particle-particle (hole-hole) part. Pairing vibrations are excited by a two-neutrons transfer operator. The Fourier analysis of the time-dependent response of the expectation value of this operator in the linear regime is used to extract strength functions. The presence of the giant pairing vibration is discussed.