487 research outputs found
Improved numerical approach for time-independent Gross-Pitaevskii nonlinear Schroedinger equation
In the present work, we improve a numerical method, developed to solve the
Gross-Pitaevkii nonlinear Schroedinger equation. A particular scaling is used
in the equation, which permits to evaluate the wave-function normalization
after the numerical solution. We have a two point boundary value problem, where
the second point is taken at infinity. The differential equation is solved
using the shooting method and Runge-Kutta integration method, requiring that
the asymptotic constants, for the function and its derivative, are equal for
large distances. In order to obtain fast convergence, the secant method is
used.Comment: 2 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
Landau damping in dilute Bose gases
Landau damping in weakly interacting Bose gases is investigated by means of
perturbation theory. Our approach points out the crucial role played by
Bose-Einstein condensation and yields an explicit expression for the decay rate
of elementary excitations in both uniform and non uniform gases. Systematic
results are derived for the phonon width in homogeneous gases interacting with
repulsive forces. Special attention is given to the low and high temperature
regimes.Comment: 11 pages, latex, 1 figure available upon request. The paper accepted
for publication in Phys. Lett.
Glueball plus Pion Production in Photon-Photon Collisions.
We here compute the reaction
for various glueball candidates and their assumed quantum states, using a
non-relativistic gluon bound-state model for the glueball.Comment: To appear in Zeit. fur Phys. C; Plain Latex file, 16 pages; 5 figures
appended as a uuencoded postscript file
Boson induced s-wave pairing in dilute boson-fermion mixtures
We show that in dilute boson-fermion mixtures with fermions in two internal
states, even when the bare fermion-fermion interaction is repulsive, the
exchange of density fluctuations of the Bose condensate may lead to an
effective fermion-fermion attraction, and thus to a Cooper instability in the
s-wave channel. We give an analytical method to derive the associated in
the limit where the phonon branch of the Bogoliubov excitation spectrum of the
bosons is important. We find a of the same order as for a pure Fermi gas
with bare attraction.Comment: 12 pages, no figure
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 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
Instantons and radial excitations in attractive Bose-Einstein condensates
Imaginary- and real-time versions of an equation for the condensate density
are presented which describe dynamics and decay of any spherical Bose-Einstein
condensate (BEC) within the mean field appraoch. We obtain quantized energies
of collective finite amplitude radial oscillations and exact numerical
instanton solutions which describe quantum tunneling from both the metastable
and radially excited states of the BEC of 7Li atoms. The mass parameter for the
radial motion is found different from the gaussian value assumed hitherto, but
the effect of this difference on decay exponents is small. The collective
breathing states form slightly compressed harmonic spectrum, n=4 state lying
lower than the second Bogolyubov (small amplitude) mode. The decay of these
states, if excited, may simulate a shorter than true lifetime of the metastable
state. By scaling arguments, results extend to other attractive BEC-s.Comment: 6 pages, 3 figure
Beyond Gross-Pitaevskii:local density vs. correlated basis approach for trapped bosons
We study the ground state of a system of Bose hard-spheres trapped in an
isotropic harmonic potential to investigate the effect of the interatomic
correlations and the accuracy of the Gross-Pitaevskii equation. We compare a
local density approximation, based on the energy functional derived from the
low density expansion of the energy of the uniform hard sphere gas, and a
correlated wave function approach which explicitly introduces the correlations
induced by the potential. Both higher order terms in the low density expansion,
beyond Gross-Pitaevskii, and explicit dynamical correlations have effects of
the order of percent when the number of trapped particles becomes similar to
that attained in recent experiments.Comment: Revtex, 2 figure
Beyond Gross-Pitaevskii:local density vs. correlated basis approach for trapped bosons
We study the ground state of a system of Bose hard-spheres trapped in an
isotropic harmonic potential to investigate the effect of the interatomic
correlations and the accuracy of the Gross-Pitaevskii equation. We compare a
local density approximation, based on the energy functional derived from the
low density expansion of the energy of the uniform hard sphere gas, and a
correlated wave function approach which explicitly introduces the correlations
induced by the potential. Both higher order terms in the low density expansion,
beyond Gross-Pitaevskii, and explicit dynamical correlations have effects of
the order of percent when the number of trapped particles becomes similar to
that attained in recent experiments.Comment: Revtex, 2 figure
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
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