B. Tanatar

Bose-Einstein condensation in a two-dimensional, trapped, interacting gas

The observation of the Bose-Einstein condensation ~BEC! phenomenon in dilute atomic gases @1‐4# has caused a lot of attention, because it provides opportunities to study the thermodynamics of weakly interacting systems in a controlled way. The condensate clouds obtained in the experiments consist of a finite number of atoms ~ranging from several thousands to several millions!, and are confined in externally applied confining potentials. The ground-state properties of the condensed gases, including the finite size effects on the temperature dependence of the condensate fraction, are of primary interest. At zero temperature, the mean-field approximation provided by the Gross-Pitaevskii equation @5# describes the condensate rather well and at finite temperatures a self-consistent Hartree-Fock-Bogoliubov ~HFB! approximation is developed @6#. Path integral Monte Carlo ~PIMC! simulations @7# on three-dimensional, interacting bosons appropriate to the current experimental conditions demonstrate the effectiveness of the mean-field-type approaches. Various aspects of the mean-field theory, as well as detailed calculations corresponding to the available experimental conditions, are discussed by Giorgini et al. @8#.

Effects of anisotropy on the critical temperature in layered nonadiabatic superconductors

The generalized anisotropic Eliashberg theory is employed to study the critical temperature of layered nonadiabatic superconductors where the relevant phonon energy is comparable to the Fermi energy. We consider a two-dimensional model appropriate for cuprate compounds and recently discovered superconductor magnesium-diboride (MgB2) which also reveals layered structure. By using the McMillan approximation we present the result of calculations of critical temperature Tc. It is shown that the critical temperature is enhanced due to the influence of anisotropy and nonadiabaticity.

Mean-field theory for Bose-Hubbard model under a magnetic field

We consider the superfluid-insulator transition for cold bosons under an effective magnetic field. We investigate how the applied magnetic field affects the Mott transition within mean-field theory and find that the critical hopping strength (t/U){sub c} increases with the applied field. The increase in the critical hopping follows the bandwidth of the Hofstadter butterfly at the given value of the magnetic field. We also calculate the magnetization and superfluid density within mean-field theory.

Bose-Einstein condensation in a one-dimensional interacting system due to power-law trapping potentials

We examine the possibility of Bose-Einstein condensation in one-dimensional interacting Bose gas subjected to confining potentials of the form

Many-body effects in the Coulomb drag between low density electron layers

V_{\rm ext}(x)=V_0(|x|/a)^\gamma

Density profile of a Bose-Einstein condensate inside a pancake-shaped trap: observational consequences of the dimensional cross-over in the scattering properties

, in which

Energy-transfer rate in Coulomb coupled quantum wires

\gamma < 2

Comparative study of screened interlayer interactions in the Coulomb drag effect in bilayer electron systems

, by solving the Gross-Pitaevskii equation within the semi-classical two-fluid model. The condensate fraction, chemical potential, ground state energy, and specific heat of the system are calculated for various values of interaction strengths. Our results show that a significant fraction of the particles is in the lowest energy state for finite number of particles at low temperature indicating a phase transition for weakly interacting systems.

Coulomb drag effect in parallel cylindrical quantum wires

Abstract Recent Coulomb drag experiments in low-density double-layer electron systems have the power of distinguishing various many-body formulations of the effective interactions. In this work we theoretically study the correlation effects on the drag resistivity in these systems within various models. The effective inter-layer interactions are best described by the generalization to the double-layer case of the Kukkonen–Overhauser approach which differs significantly from the self-consistent field approach of Singwi et al. [Phys. Rev. 176 (1968) 589]. Following the formulation of Vignale and Singwi [Phys. Rev. B 32 (1985) 2156] we derive an expression for the effective inter-layer interaction which embodies the many-body correlations through the local-field corrections. The drag resistivity is calculated within this approach together with the Hubbard approximation for the intra-layer local-field factor and a simple model for the inter-layer correlations. Comparison with the recent measurements of Kellogg et al. [Solid State Commun. 123 (2002) 515] yields very good agreement. Our results are also contrasted with the corresponding drag resistivities given by the Singwi et al. theory, the dynamic random-phase approximation and the Hubbard approximation. The significant differences found between these theories emphasize the strong sensitivity of the drag resistivity to the effective inter-layer interactions.

COLLECTIVE MODES IN A QUASI-ONE-DIMENSIONAL, TWO-COMPONENT ELECTRON LIQUID

Abstract It is theoretically well known that two-dimensionality of the scattering events in a Bose–Einstein condensate introduces a logarithmic dependence on density in the coupling constant entering a mean-field theory of the equilibrium density profile, which becomes dominant as the s -wave scattering length gets larger than the condensate thickness. We trace the regions of experimentally accessible system parameters for which the cross-over between different dimensionality behaviors in the scattering properties may become observable through in situ imaging of the condensed cloud with varying trap anisotropy and scattering length.