The q-deformed Bose gas: Integrability and thermodynamics

We investigate the exact solution of the q-deformed one-dimensional Bose gas to derive all integrals of motion and their corresponding eigenvalues. As an application, the thermodynamics is given and compared to an effective field theory at low temperatures.Comment: 10 pages, 6 figure

Self-consistent calculation of the coupling constant in the Gross-Pitaevskii equation

A method is proposed for a self-consistent evaluation of the coupling constant in the Gross-Pitaevskii equation without involving a pseudopotential replacement. A renormalization of the coupling constant occurs due to medium effects and the trapping potential, e.g. in quasi-1D or quasi-2D systems. It is shown that a simplified version of the Hartree-Fock-Bogoliubov approximation leads to a variational problem for both the condensate and a two-body wave function describing the behaviour of a pair of bosons in the Bose-Einstein condensate. The resulting coupled equations are free of unphysical divergences. Particular cases of this scheme that admit analytical estimations are considered and compared to the literature. In addition to the well-known cases of low-dimensional trapping, cross-over regimes can be studied. The values of the kinetic, interaction, external, and release energies in low dimensions are also evaluated and contributions due to short-range correlations are found to be substantial.Comment: 15 pages, ReVTEX, no figure

Universality of the one dimensional Bose gas with delta interaction

We consider several models of interacting bosons in a one dimensional lattice. Some of them are not integrable like the Bose-Hubbard others are integrable. At low density all of these models can be described by the Bose gas with delta interaction. The lattice corrections corresponding to the different models are contrasted.Comment: 6 pages, no figures; minor changes; refs. adde

On the 'Strong-Coupling' Generalization of the Bogoliubov Model

A generalized Bogoliubov model of the Bose gas in the ground state is proposed which properly takes into account both the long-range and short-range spatial boson correlations. It concerns equilibrium characteristics and operates with in-medium Schrodinger equations for the pair wave functions of bosons being the eigenfunctions of the second-order reduced density matrix. The approach developed provides reasonable results for a dilute Bose gas with arbitrary strong interaction between particles (the 'strong-coupling' case) and comes to the canonical Bogoliubov model in the weak-coupling regime.Comment: 6 pages, REVTEX, no figure

Analytic perturbation theory versus 1/N expansion in the Gross-Neveu model

The 1/N expansion can be successfully used to calculate the Green functions of the two-dimensional O(2N) Gross - Neveu model. In parallel, the methods of analytic perturbation theory are also applied. Comparing the results of these two calculations at leading order, we report on the surprising agreement between them.Comment: Latex, 3 figures, 4 page

Bose-Einstein-condensed gases with arbitrary strong interactions

Bose-condensed gases are considered with an effective interaction strength varying in the whole range of the values between zero and infinity. The consideration is based on the usage of a representative statistical ensemble for Bose systems with broken global gauge symmetry. Practical calculations are illustrated for a uniform Bose gas at zero temperature, employing a self-consistent mean-field theory, which is both conserving and gapless.Comment: Latex file, 23 pages, 4 figure

Non-perturbative solutions in the electro-weak theory with tˉt\bar t t condensate and the tt-quark mass

We apply Bogoliubov compensation principle to the gauge electro-weak interaction to demonstrate a spontaneous generation of anomalous three-boson gauge invariant effective interaction. The non-trivial solution of compensation equations uniquely defines the form-factor of the anomalous interaction and parameters of the theory including value of gauge electro-weak coupling $g(M_W^2)$ in satisfactory agreement with its experimental value. A possibility of spontaneous generation of effective four-fermion interaction of heavy quarks is also demonstrated. This interaction defines an equation for a scalar bound state of heavy quarks which serve as a substitute for the elementary scalar Higgs doublet. As a result we calculate the $t$-quark mass $m_t\,=\,177\,GeV$ in satisfactory agreement with the experimental value. The results strongly support idea of $\bar t\,t$ condensate as a source of the electro-weak symmetry breaking.Comment: 16 pages, 5 figures. arXiv admin note: substantial overlap with arXiv:1103.395

CDF Wjj anomaly as a non-perturbative effect of the electro-weak interaction

The recently reported CDF excess at $120\,-\, 160\,GeV$ in invariant mass distribution of jet pairs accompanying $W$-boson is tentatively interpreted as a bound state of two $W$ decaying to quark-anti-quark pair. Non-perturbative effects of EW interaction obtained by application of Bogoliubov compensation approach lead to such bound state due to existence of anomalous three-boson gauge-invariant effective interaction. The application of this scheme gives satisfactory agreement with existing data without any adjusting parameter but the bound state mass $145\,GeV$.Comment: 5 pages, 2 figure