The Hartree-Fock-Bogoliubov equation for the ground states of even-even atomic nuclei is solved using the canonical representation in the coordinate space for zero range interactions like the Skyrme force. The gradient method is improved for faster convergence to the solutions under constraint of orthogonality between canonical orbitals. Necessity of the cut-off of the pairing interaction is sh...

We have developed a semiclassical approach to solving the Bogoliubov-de Gennes equations for superconductors. It is based on the study of classical orbits governed by an effective Hamiltonian corresponding to the quasiparticles in the superconducting state and includes an account of the Bohr-Sommerfeld quanti-sation rule, the Maslov index, torus quantisation, topological phases arising from lin...

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...

We present a new method of calculating the distribution function and fluctuations for a Bose-Einstein condensate (BEC) of N interacting atoms. The present formulation combines our previous master equation and canonical ensemble quasiparticle techniques. It is applicable both for ideal and interacting Bogoliubov BEC and yields remarkable accuracy at all temperatures. For the interacting gas of 2...

Superdeformed states in light N = Z nuclei are studied by means of the self-consistent cranking calculation (i.e., the P+QQ model based on the cranked Hartree-Fock-Bogoliubov method). Analyses are given for two typical cases of superdeformed bands in the A 40 mass region, that is, bands where backbending is absent (40Ca) or present (36Ar). Investigations are carried out particularly for the fol...

Following the ideas N. Bogoliubov used to derive classical and quantum nonlinear kinetic equations, we Redfield linear master equation, which is widely in theory of open systems. This method allows one calculate joint state a system reservoir at every instant time, as well obtain equations autonomous differential an arbitrary order perturbation theory. We prove that under certain conditions exp...

Cranked Relativistic Hartree-Bogoliubov theory without and with approximate particle number projection by means of the Lipkin-Nogami method is presented in detail as an extension of Relativistic Mean Field theory with pairing correlations to the rotating frame. Pairing correlations are taken into account by a finite range two-body force of Gogny type. The applicability of this theory to the des...

It is found that combining an excitation-energy sum rule with Fetter’s trial wave function gives almost exact low-lying collective-mode frequencies of a trapped Bose-Einstein condensate at zero temperature. Realizations of Bose-Einstein condensation (BEC) in trapped atomic gases1–4 have enabled us to study many-body physics of weakly interacting bosons with unprecedented precision. Experiments ...