Dynamics of Collapse of a Confined Bose Gas

Rigorous results on the nonlinear dynamics of a dilute Bose gas with a negative scattering length in an harmonic magnetic trap are presented and sufficient conditions for the collapse of the system are formulated. By using the virial theorem for the Gross-Pitaevskii equations in an external field we analyze the temporal evolution of the mean square radius of the gas cloud. In the 2D case the quantity undergoes harmonic oscillation with frequency $2\omega _0$ It implies that for a negative value of energy of the system, the gas cloud will collapse after a finite time interval. For positive energy the cloud collapses if the initial conditions correspond to a large enough amplitude of oscillations. Stable oscillations with a small amplitude are possible. In the 3D case the system also collapsed after a finite time for a state with negative energy. A stringent condition for the collapse is also derived.Comment: 10 pages, REVTEX, 2 figures (available upon request

TWO NEW SHORT-PERIOD CEPHEIDS

The General Catalogue of Variable Stars gives periods of slightly less than three-quarters of a day for the stars NO Cas and CN Tau. However, new photometry demonstrates that their periods are actually 2.6 and 1.8 days, respectively, and they are thus classical Cepheids. Fourier decompositions of their light curves are performed, and they are found to be members of a class of Cepheids with periods less than three days which may be related to the s-Cepheids. These two stars represent the shortest and longest known members of this class and thus are very useful in defining its properties in the Fourier diagrams

Output from Bose condensates in tunnel arrays: the role of mean-field interactions and of transverse confinement

We present numerical studies of atomic transport in 3D and 1D models for a mode-locked, pulsed atom laser as realized by Anderson and Kasevich [Science 281 (1998) 1686] using an elongated Bose condensate of ${}^{87}$Rb atoms poured into a vertical optical lattice. From our 3D results we ascertain in a quantitative manner the role of mean-field interactions in determining the shape and the size of the pulses in the case of Gaussian transverse confinement. By comparison with 1D simulations we single out a best-performing 1D reduction of the mean-field interactions, which yields quantitatively useful predictions for all main features of the matter output.Comment: 12 pages, 2 figure

Stability of Solution of the Nonlinear Schr\"odinger Equation for the Bose-Einstein Condensation

We investigate the stability of the Bose-Einstein condensate (BEC) the case of atoms with negative scattering lengths at zero temperature using the Ginzburg-Pitaevskii-Gross (GPG) stationary theory. We have found a new exact equation for determining the upper bound of the critical numbers $N_{cr}$ of atoms for a metastable state to exist. Our calculated value of $N_{cr}$ for Bose-Einstein condensation of lithium atoms based on our new equation is in agreement with those observed in a agreement with those observed in a recent experiment.Comment: 8 pages, Late

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

Bose-Einstein condensation thermodynamics of a trapped gas with attractive interaction

We study the Bose-Einstein condensation of an interacting gas with attractive interaction confined in a harmonic trap using a semiclassical two-fluid mean-field model. The condensed state is described by converged numerical solution of the Gross-Pitaevskii equation. By solving the system of coupled equations of this model iteratively we obtain converged results for the temperature dependencies of the condensate fraction, chemical potential, and internal energy for the Bose-Einstein condensate of $^7$Li atoms.Comment: Five latex pages, four postscript figures, Accepted in Physica

Self-Trapping, Quantum Tunneling and Decay Rates for a Bose Gas with Attractive Nonlocal Interaction

We study the Bose-Einstein condensation for a cloud of $^7$Li atoms with attractive nonlocal (finite-range) interaction in a harmonic trap. In addition to the low-density metastable branch, that is present also in the case of local interaction, a new stable branch appears at higher densities. For a large number of atoms, the size of the cloud in the stable high-density branch is independent of the trap size and the atoms are in a macroscopic quantum self-trapped configuration. We analyze the macroscopic quantum tunneling between the low-density metastable branch and the high-density one by using the istanton technique. Moreover we consider the decay rate of the Bose condensate due to inelastic two- and three-body collisions.Comment: 5 pages, 4 figures, submitted to Phys. Rev.

Small-amplitude normal modes of a vortex in a trapped Bose-Einstein condensate

We consider a cylindrically symmetric trap containing a small Bose-Einstein condensate with a singly quantized vortex on the axis of symmetry. A time-dependent variational Lagrangian analysis yields the small-amplitude dynamics of the vortex and the condensate, directly determining the equations of motion of the coupled normal modes. As found previously from the Bogoliubov equations, there are two rigid dipole modes and one anomalous mode with a negative frequency when seen in the laboratory frame.Comment: 4 pages, no figures, Revte