Low Density Limit of BCS Theory and Bose-Einstein Condensation of Fermion Pairs

We consider the low density limit of a Fermi gas in the BCS approximation. We show that if the interaction potential allows for a two-particle bound state, the system at zero temperature is well approximated by the Gross-Pitaevskii functional, describing a Bose-Einstein condensate of fermion pairs.Comment: LaTeX2e, 17 page

Momentum-Transfer to and Elementary-Excitations of a Bose-Einstein Condensate by a Time-Dependent Optical Potential

We present results of calculations on Bose-Einstein condensed $^{87}$Rb atoms subjected to a moving standing-wave light-potential of the form $V_L(z,t) = V_0(t) \cos(q z-\omega t)$. We calculate the mean-field dynamics (the order paramter) of the condensate and determine the resulting condensate momentum in the $z$ direction, $P_z(q,\omega,V_0,t_p)$, where $V_0$ is the peak optical potential strength and $t_p$ is the pulse duration. Although the local density approximation for the Bogoliubov excitation spectral distribution is a good approximation for very low optical intensities, long pulse duration and sufficiently large values of the wavevector $q$ of the light-potential, for small $q$, short duration pulses, or for not-so-low intensities, the local density perturbative description of the excitation spectrum breaks down badly, as shown by our results.Comment: 8 pages, 7 figure

Violation of self-similarity in the expansion of a 1D Bose gas

The expansion of a 1D Bose gas is investigated employing the Lieb-Liniger equation of state within the local density approximation. We show that during the expansion the density profile of the gas does not follow a self-similar solution, as one would expect from a simple scaling Ansatz. We carry out a variational calculation, which recovers the numerical results for the expansion, the equilibrium properties of the density profile, and the frequency of the lowest compressional mode. The variational approach allows for the analysis of the expansion in all interaction regimes between the mean field and the Tonks-Girardeau limits, and in particular shows the range of parameters for which the expansion violates self-similarity.Comment: 6 pages, 5 eps figure

Universal physics of 2+1 particles with non-zero angular momentum

The zero-energy universal properties of scattering between a particle and a dimer that involves an identical particle are investigated for arbitrary scattering angular momenta. For this purpose, we derive an integral equation that generalises the Skorniakov - Ter-Martirosian equation to the case of non-zero angular momentum. As the mass ratio between the particles is varied, we find various scattering resonances that can be attributed to the appearance of universal trimers and Efimov trimers at the collisional threshold.Comment: 6 figure

Vortex states in binary mixture of Bose-Einstein condensates

The vortex configurations in the Bose-Einstein condensate of the mixture of two different spin states |F=1,m_f=-1> and |2,1> of ^{87}Rb atoms corresponding to the recent experiments by Matthews et. al. (Phys. Rev. Lett. 83, 2498 (1999)) are considered in the framework of the Thomas-Fermi approximation as functions of N_2/N_1, where N_1 is the number of atoms in the state |1,-1> and N_2 - in the state |2,1>. It is shown that for nonrotating condensates the configuration with the |1,-1> fluid forming the shell about the |2,1> fluid (configuration "a") has lower energy than the opposite configuration (configuration "b") for all values of N_2/N_1. When the |1,-1> fluid has net angular momentum and forms an equatorial ring around the resting central condensate |2,1>, the total energy of the system is higher than the ground energy, but the configuration "a" has lower energy than the configuration "b" for all N_2/N_1. On the other hand, when the |2> fluid has the net angular momentum, for the lowest value of the angular momentum \hbar l (l=1) there is the range of the ratio N_2/N_1 where the configuration "b" has lower energy than the configuration "a". For higher values of the angular momentum the configuration "b" is stable for all values of N_2/N_1.Comment: minor changes, references adde

Hydrodynamic Approach to Vortex Lifetime in Trapped Bose Condensates

We study a vortex in a two-dimensional, harmonically trapped Bose-Einstein condensate at zero temperature. Through a variational calculation using a trial condensate wave function and a nonlinear Schroedinger Lagrangian, we obtain the effective potential experienced by a vortex at an arbitrary position in the condensate, and find that an off-center vortex will move in a circular trajectory around the trap center. We find the frequency of this precession to be smaller than the elementary excitation frequencies in the cloud. We also study the radiation of sound from a moving vortex in an infinite, uniform system, and discuss the validity of this as an approximation for the trapped case. Furthermore, we estimate the lifetime of a vortex due to imperfections in the trapping potential.Comment: 10 pages, 1 eps figure, submitted to PRA, adjustments in response to referee, one refernce adde

Light-like noncommutativity and duality from open strings/branes

In this paper we perform some non-trivial tests for the recently obtained open membrane/D-brane metrics and `generalized' noncommutativity parameters using Dp/NS5/M5-branes which have been deformed by light-like fields. The results obtained give further evidence that these open membrane/D-brane metrics and `generalized' noncommutativity parameters are correct. Further, we use the open brane data and supergravity duals to obtain more information about non-gravitational theories with light-like noncommutativity, or `generalized' light-like noncommutativity. In particular, we investigate various duality relations (strong coupling limits). In the light-like case we also comment on the relation between open membrane data (open membrane metric etc.) in six dimensions and open string data in five dimensions. Finally, we investigate the strong coupling limit (high energy limit) of five dimensional NCYM with \Theta^{12}=\Theta^{34}. In particular, we find that this NCYM theory can be UV completed by a DLCQ compactification of M-theory.Comment: 24 pages, Latex. v2:Comments and references added. v3:Version published in JHE

Ising spins coupled to a four-dimensional discrete Regge skeleton

Regge calculus is a powerful method to approximate a continuous manifold by a simplicial lattice, keeping the connectivities of the underlying lattice fixed and taking the edge lengths as degrees of freedom. The discrete Regge model employed in this work limits the choice of the link lengths to a finite number. To get more precise insight into the behavior of the four-dimensional discrete Regge model, we coupled spins to the fluctuating manifolds. We examined the phase transition of the spin system and the associated critical exponents. The results are obtained from finite-size scaling analyses of Monte Carlo simulations. We find consistency with the mean-field theory of the Ising model on a static four-dimensional lattice.Comment: 19 pages, 7 figure

Temperature-induced resonances and Landau damping of collective modes in Bose-Einstein condensed gases in spherical traps

Interaction between collective monopole oscillations of a trapped Bose-Einstein condensate and thermal excitations is investigated by means of perturbation theory. We assume spherical symmetry to calculate the matrix elements by solving the linearized Gross-Pitaevskii equations. We use them to study the resonances of the condensate induced by temperature when an external perturbation of the trapping frequency is applied and to calculate the Landau damping of the oscillations.Comment: revtex, 9 pages, 5 figure

Stability of Repulsive Bose-Einstein Condensates in a Periodic Potential

The cubic nonlinear Schr\"odinger equation with repulsive nonlinearity and an elliptic function potential models a quasi-one-dimensional repulsive dilute gas Bose-Einstein condensate trapped in a standing light wave. New families of stationary solutions are presented. Some of these solutions have neither an analog in the linear Schr\"odinger equation nor in the integrable nonlinear Schr\"odinger equation. Their stability is examined using analytic and numerical methods. All trivial-phase stable solutions are deformations of the ground state of the linear Schr\"odinger equation. Our results show that a large number of condensed atoms is sufficient to form a stable, periodic condensate. Physically, this implies stability of states near the Thomas-Fermi limit.Comment: 12 pages, 17 figure