By means of the extended Krylov-Bogoliubov-Mitropolskii method, an asymptotic solution second order over-damped nonlinear system is found. The results obtained by this method are exactly same as Murty et al. (1969). determination followed (1969) too much laborious and cumbersome. On contrary, present very simple easier. It illustrated example.

The coordinate-space representation of the Hartree-Fock-Bogoliubov theory is method choice to study weakly bound nuclei whose properties are affected by quasiparticle continuum space. To describe such systems, we developed a three-dimensional Skyrme-Hartree-Fock-Bogoliubov solver HFBFFT based on existing, highly optimized and parallelized Skyrme-Hartree-Fock code Sky3D. does not impose any self...

All possible Bogoliubov operators that generate the thermal transformations in Thermo Field Dynamics (TFD) form a SU (1, 1) group. We discuss this construction in the bosonic string theory. In particular, the transformation of the Fock space and string operators generated by the most general SU(1, 1) unitary Bogoliubov transformation and the entropy of the corresponding thermal string are compu...

We review the superfluid to Mott-insulator transition of cold atoms in optical lattices. The experimental signatures of the transition are discussed and the RPA theory of the Bose-Hubbard model briefly described. We point out that the critical behavior at the transition, as well as the prediction by the RPA theory of a gapped mode (besides the Bogoliubov sound mode) in the superfluid phase, are...

The key insight of Bogoliubov is that although the mean-field Hamiltonian (1) is clearly not diagonal in the space of states created by the operators ck,↑/↓, it may be diagonal in a basis of states created by operators related to these via a simple SU2 transformation. Indeed, it may be the case that ‘electrons’ and ‘holes’ are the wrong degrees of freedom to consider; we should at least look to...

The existing formalism used to compute the operator overlaps necessary carry out generator coordinate method calculations using a set of Hartree- Fock- Bogoliubov wave functions, is generalized case where each HFB states are expanded in different arbitrary bases spanning sub-space Hilbert space.

We investigate the large-N behaviour of simple examples of supersymmetric interactions for fermions on a lattice. Witten’s supersymmetric quantum mechanics and the BCS model appear just as two different aspects of one and the same model. For the BCS model, supersymmetry is only respected in a coherent superposition of Bogoliubov states. In this coherent superposition mesoscopic observables show...

The Bogoliubov transformation in thermofield dynamics, an operator formalism for the finite-temperature quantum-field theory, is generalized to describe a field in arbitrary confined regions of space and time. Starting with the scalar field, the approach is extended to the electromagnetic field and the energy-momentum tensor is written via the Bogoliubov transformation. In this context, the Cas...