Order Parameter at the Boundary of a Trapped Bose Gas

Through a suitable expansion of the Gross-Pitaevskii equation near the classical turning point, we obtain an explicit solution for the order parameter at the boundary of a trapped Bose gas interacting with repulsive forces. The kinetic energy of the system, in terms of the classical radius $R$ and of the harmonic oscillator length $a_{_{HO}}$, follows the law $E_{kin}/N \propto R^{-2} [\log (R/a_{_{HO}}) + \hbox{const.}]$, approaching, for large $R$, the results obtained by solving numerically the Gross-Pitaevskii equation. The occurrence of a Josephson-type current in the presence of a double trap potential is finally discussed.Comment: 11 pages, REVTEX, 4 figures (uuencoded-gzipped-tar file) also available at http://anubis.science.unitn.it/~dalfovo/papers/papers.htm

Bosons in anisotropic traps: ground state and vortices

We solve the Gross-Pitaevskii equations for a dilute atomic gas in a magnetic trap, modeled by an anisotropic harmonic potential. We evaluate the wave function and the energy of the Bose Einstein condensate as a function of the particle number, both for positive and negative scattering length. The results for the transverse and vertical size of the cloud of atoms, as well as for the kinetic and potential energy per particle, are compared with the predictions of approximated models. We also compare the aspect ratio of the velocity distribution with first experimental estimates available for $^{87}$Rb. Vortex states are considered and the critical angular velocity for production of vortices is calculated. We show that the presence of vortices significantly increases the stability of the condensate in the case of attractive interactions.Comment: 22 pages, REVTEX, 8 figures available upon request or at http://anubis.science.unitn.it/~dalfovo/papers/papers.htm

Exciting, Cooling And Vortex Trapping In A Bose-Condensed Gas

A straight forward numerical technique, based on the Gross-Pitaevskii equation, is used to generate a self-consistent description of thermally-excited states of a dilute boson gas. The process of evaporative cooling is then modelled by following the time evolution of the system using the same equation. It is shown that the subsequent rethermalisation of the thermally-excited state produces a cooler coherent condensate. Other results presented show that trapping vortex states with the ground state may be possible in a two-dimensional experimental environment.Comment: 9 pages, 7 figures. It's worth the wait! To be published in Physical Review A, 1st February 199

Condensate fraction and critical temperature of a trapped interacting Bose gas

By using a mean field approach, based on the Popov approximation, we calculate the temperature dependence of the condensate fraction of an interacting Bose gas confined in an anisotropic harmonic trap. For systems interacting with repulsive forces we find a significant decrease of the condensate fraction and of the critical temperature with respect to the predictions of the non-interacting model. These effects go in the opposite direction compared to the case of a homogeneous gas. An analytic result for the shift of the critical temperature holding to first order in the scattering length is also derived.Comment: 8 pages, REVTEX, 2 figures, also available at http://anubis.science.unitn.it/~oss/bec/BEC.htm

Mass Dependent αS\alpha_S Evolution and the Light Gluino Existence

There is an intriguing discrepancy between \alpha_s(M_Z) values measured directly at the CERN $Z_0$-factory and low-energy (at few GeV) measurements transformed to $Q=M_{Z_0}$ by a massless QCD \alpha_s(Q) evolution relation. There exists an attempt to reconcile this discrepancy by introducing a light gluino \gl in the MSSM. We study in detail the influence of heavy thresholds on \alpha_s(Q) evolution. First, we consruct the "exact" explicit solution to the mass-dependent two-loop RG equation for the running \alpha_s(Q). This solution describes heavy thresholds smoothly. Second, we use this solution to recalculate anew \alpha_s(M_Z) values corresponding to "low-energy" input data. Our analysis demonstrates that using {\it mass-dependent RG procedure} generally produces corrections of two types: Asymptotic correction due to effective shift of threshold position; Local threshold correction only for the case when input experiment lies in the close vicinity of heavy particle threshold: $Q_{expt} \simeq M_h$. Both effects result in the effective shift of the \asmz values of the order of $10^{-3}$. However, the second one could be enhanced when the gluino mass is close to a heavy quark mass. For such a case the sum effect could be important for the discussion of the light gluino existence as it further changes the \gl mass.Comment: 13, Late

Conserving and Gapless Approximations for an Inhomogeneous Bose Gas at Finite Temperatures

We derive and discuss the equations of motion for the condensate and its fluctuations for a dilute, weakly interacting Bose gas in an external potential within the self--consistent Hartree--Fock--Bogoliubov (HFB) approximation. Account is taken of the depletion of the condensate and the anomalous Bose correlations, which are important at finite temperatures. We give a critical analysis of the self-consistent HFB approximation in terms of the Hohenberg--Martin classification of approximations (conserving vs gapless) and point out that the Popov approximation to the full HFB gives a gapless single-particle spectrum at all temperatures. The Beliaev second-order approximation is discussed as the spectrum generated by functional differentiation of the HFB single--particle Green's function. We emphasize that the problem of determining the excitation spectrum of a Bose-condensed gas (homogeneous or inhomogeneous) is difficult because of the need to satisfy several different constraints.Comment: plain tex, 19 page

Testing quantum correlations in a confined atomic cloud by scattering fast atoms

We suggest measuring one-particle density matrix of a trapped ultracold atomic cloud by scattering fast atoms in a pure momentum state off the cloud. The lowest-order probability of the inelastic process, resulting in a pair of outcoming fast atoms for each incoming one, turns out to be given by a Fourier transform of the density matrix. Accordingly, important information about quantum correlations can be deduced directly from the differential scattering cross-section. A possible design of the atomic detector is also discussed.Comment: 5 RevTex pages, no figures, submitted to PR

Stability of the trapped nonconservative Gross-Pitaevskii equation with attractive two-body interaction

The dynamics of a nonconservative Gross-Pitaevskii equation for trapped atomic systems with attractive two-body interaction is numerically investigated, considering wide variations of the nonconservative parameters, related to atomic feeding and dissipation. We study the possible limitations of the mean field description for an atomic condensate with attractive two-body interaction, by defining the parameter regions where stable or unstable formation can be found. The present study is useful and timely considering the possibility of large variations of attractive two-body scattering lengths, which may be feasible in recent experiments.Comment: 6 pages, 5 figures, submitted to Physical Review

Spectral method for the time-dependent Gross-Pitaevskii equation with a harmonic trap

We study the numerical resolution of the time-dependent Gross-Pitaevskii equation, a non-linear Schroedinger equation used to simulate the dynamics of Bose-Einstein condensates. Considering condensates trapped in harmonic potentials, we present an efficient algorithm by making use of a spectral Galerkin method, using a basis set of harmonic oscillator functions, and the Gauss-Hermite quadrature. We apply this algorithm to the simulation of condensate breathing and scissors modes.Comment: 23 pages, 5 figure

Current-density functional for disordered systems

The effective action for the current and density is shown to satisfy an evolution equation, the functional generalization of Callan-Symanzik equation. The solution describes the dependence of the one-particle irreducible vertex functions on the strength of the quenched disorder and the annealed Coulomb interaction. The result is non-perturbative, no small parameter is assumed. The a.c. conductivity is obtained by the numerical solution of the evolution equation on finite lattices in the absence of the Coulomb interaction. The static limit is performed and the conductivity is found to be vanishing beyond a certain threshold of the impurity strength.Comment: final version, 28 pages, 17 figures, to appear in Phys. Rev.