We present the microscopic kinetic theory of a homogeneous dilute Bose condensed gas in the generalized random phase approximation (GRPA), which satisfies the following requirements: 1) the mass, momentum and energy conservation laws; 2) the H-theorem; 3) the superfluidity property and 4) the recovery of the Bogoliubov theory at zero temperature . In this approach, the condensate influences the...

We study the problem of Bose condensation at zero temperature and weak coupling for a three dimensional system of bosons, interacting with a repulsive short range potential, in the Bogoliubov approximation. We prove that the properties of the model can be explained in terms of an anomalous asymptotically free renormalization group ow and we show that the two-point correlation function has the t...

We perform a multimode treatment of spin squeezing induced by interactions in atomic condensates, and we show that, at finite temperature, the maximum spin squeezing has a finite limit when the atom number N → ∞ at fixed density and interaction strength. To calculate the limit of the squeezing parameter for a spatially homogeneous system we perform a double expansion with two small parameters: ...

We investigate the superfluid properties of a Bose–Einstein condensate (BEC) trapped in a one-dimensional periodic potential. We study, both analytically (in the tight binding limit) and numerically, the Bloch chemical potential, the Bloch energy and the Bogoliubov dispersion relation, and we introduce two different, density dependent, effective masses and group velocities. The Bogoliubov spect...

It is well-known that in bulk, the solution of the Bogoliubov-de Gennes equations is the same whether or not the Hartree-Fock term is included. In this case the Hartree-Fock potential is position independent and, so, gives the same contribution to both the single-electron energies and the Fermi level (the chemical potential). Thus, the single-electron energy measured from the Fermi level (it co...

We show that, in finite dimensions, the only monotone metrics on the space of invertible density matrices for which the (+1) and (−1) affine connections are mutually dual are constant multiples of the Bogoliubov-Kubo-Mori metric.

The objective of this paper is to consider the dynamic motions of second order, weakly non-linear, discrete systems. The main attention is focused on a comparison, for such systems, of the method of Krylov–Bogoliubov (KB) and an enhanced Galerkin (EG) method which produce seemingly different solutions. Despite the apparent differences, the two methods are shown to give identical first order per...

We theoretically generalize a systematic language to describe the phase-imprinting technique investigate dynamical generation of solitons in one-dimensional Raman-type spin-orbit-coupled Fermi superfluid. check our method with simulation time-dependent Bogoliubov--de Gennes equations and find that not only can generate stable dark even gray conventional superfluid by controlling transferred pha...

JAPAN In this paper, we consider Bogoliubov automorphisms of CAR algebra and we give imple-menters as continuous linear operators on the white noise (test or generalized) functionals for the Fermion system with the help of the Fock expansion.