The Bogoliubov procedure in quantum field theory is used to describe a relativistic almost ideal Bose gas at zero temperature. Special attention is given to the study of a vortex. The radius of the vortex in the field description is compared to that obtained in the relativistic fluid approximation. The Kelvin waves are studied and, for long wavelengths, the dispersion relation is obtained by an...

with a symmetric and positive definite operator A defined on a Hilbert space V with dimV = N and its preconditioned version PCG. We derive the CG from the projection in A-inner product point of view. We shall use (·, ·) for the standard inner product and (·, ·)A for the inner product introduced by the SPD operator A. When we say ‘orthogonal’ vectors, we refer to the default (·, ·) inner product...

A technique is developed for obtaining the solution of second order over-damped non-linear systems based on Krylov-Bogoliubov-Mitropolskii (KBM) method small ratio eigenvalues. The also useful large illustrated by an example.

A C++ code for the solution of the relativistic Hartree-Bogoliubov theory in coordinatespace is presented. The theory describes a nucleus as a relativistic system of baryons andmesons. The RHB model is applied in the self-consistent mean-field approximation to thedescription of ground state properties of spherical nuclei. Finite range interactions areincluded to describe pai...

We discuss the Bogoliubov transformation of the scalar wave functions caused by the change of coordinates in 4 dimensional de Sitter space. It is shown that the exact Bogoliubov coefficients can be obtained from the global coordinates to the static coordinates where there exist manifest horizon. We consider two type of global coordinates. In one global coordinates, it is shown that the Bogoliub...

The angular momentum projection (AMP) method is implemented in the deformed relativistic Hartree-Bogoliubov theory continuum (DRHBc) with point-coupling density functional. wave functions of projected states are expanded terms Dirac Woods-Saxon (WS) basis, providing a proper description asymptotic behavior functions. contribution induced by pairing considered treating correlation Bogoliubov tra...

The Bogoliubov transformation for a monopole boson induces an unitary connecting the Fock spaces of initial and correlated boson-s. Here we provide very simple method deriving analytical expression overlap matrix basis states generating two spaces.

We study the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) superconducting state in the disordered systems. We analyze the microscopic model, in which the dwave superconductivity is stabilized near the antiferromagnetic quantum critical point, and investigate two kinds of disorder, namely, box disorder and point disorder, on the basis of the Bogoliubov-deGennes (BdG) equation. The spatial structure of...

Consider the eigenvalue problem QAQ~x = λ~x, where A is an n×n matrix and Q is projection matrix onto a subspace S⊥ of dimension n−k. In this paper we construct a meromorphic function whose zeros correspond to the (generically) n−k nonzero eigenvalues of QAQ. The construction of this function requires only that we know A and a basis for S, the orthogonal complement of S⊥. The formulation of the...