The kinetic and interaction energies of a trapped Bose gas: Beyond the mean field

The kinetic and interaction energies of a three-dimensional dilute ground-state Bose gas confined in a trap are calculated beyond a mean-field treatment. They are found to depend on the pairwise interaction trough two characteristic lengths: the first, a, is the well-known scattering length and the second, b, is related to the latter by b=a-\lambda d a/d\lambda with \lambda being the coupling constant. Numerical estimations show that the pairwise interaction energy of a dilute gas of alkali atoms in a trap is negative (in spite of the positive scattering length); its absolute value is found by about the order of magnitude larger than that of the mean-field interaction energy that corresponds to the last term in the Gross-Pitaevskii functional.Comment: 5 pages, REVTeX, 1 figure inserte

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

Dilute Bose gas in two dimensions: Density expansions and the Gross-Pitaevskii equation

A dilute two-dimensional (2D) Bose gas at zero temperature is studied by the method developed earlier by the authors. Low density expansions are derived for the chemical potential, ground state energy, kinetic and interaction energies. The expansion parameter is found to be a dimensionless in-medium scattering amplitude u obeying the equation 1/u+\ln u=-\ln(na^2\pi)-2\gamma, where na^2 and \gamma are the gas parameter and the Euler constant, respectively. It is shown that the ground state energy is mostly kinetic in the low density limit; this result does not depend on a specific form of the pairwise interaction potential, contrary to 3D case. A new form of 2D Gross-Pitaevskii equation is proposed within our scheme.Comment: 4 pages, REVTeX, no figure

On the Momentum Distribution and Condensate Fraction in the Bose Liquid

The model recently proposed by A.A. Shanenko [Phys. Lett. A 227 (1997) 367] is used to derive linear integro-differential equations whose solutions provide reasonable estimates for the momentum distribution and condensate fraction in interacting many-boson system at zero temperature. An advantage of these equations is that they can be employed in the weak coupling regime and beyond. As an example, analytical treatment of the weak coupling case is given.Comment: 12 pages, REVTEX, no figures, submitted to Phys. Lett.

Quasicondensate and superfluid fraction in the 2D charged-boson gas at finite temperature

The Bogoliubov - de Gennes equations are solved for the Coulomb Bose gas describing a fluid of charged bosons at finite temperature. The approach is applicable in the weak coupling regime and the extent of its quantitative usefulness is tested in the three-dimensional fluid, for which diffusion Monte Carlo data are available on the condensate fraction at zero temperature. The one-body density matrix is then evaluated by the same approach for the two-dimensional fluid with e^2/r interactions, to demonstrate the presence of a quasi-condensate from its power-law decay with increasing distance and to evaluate the superfluid fraction as a function of temperature at weak coupling.Comment: 9 pages, 2 figure

Pairing in two-dimensional boson-fermion mixtures

The possibilities of pairing in two-dimensional boson-fermion mixtures are carefully analyzed. It is shown that the boson-induced attraction between two identical fermions dominates the p-wave pairing at low density. For a given fermion density, the pairing gap becomes maximal at a certain optimal boson concentration. The conditions for observing pairing in current experiments are discussedComment: 10 pages, 5 figs, revtex

Structure of Organosilicon Dendrimers of Higher Generations

The structure of organosilicon dendrimers of the ninth generation with the four-functional core and butyl terminal groups has been studied by small-angle neutron scattering. It has been demonstrated that the dendrimers are monodisperse objects with an anisometric shape. The partial volume and the average scattering density have been determined using the contrast variation technique. It has been shown that the dendrimers under study are identical in overall sizes and scattering density distribution. It has been revealed that 20% of the overall volume of the dendrimer is accessible for the penetration of the solvent. The distribution of the scattering length density in the dendrimers has been simulated and reconstructed using the Monte Carlo method, and a change in the excluded volume for different contrasts has been revealed. The specific features of the spatial structure of organosilicon dendrimers of higher generations have been discussed