5,566 research outputs found
Static Einstein-Maxwell Solutions in 2+1 dimensions
We obtain the Einstein-Maxwell equations for (2+1)-dimensional static
space-time, which are invariant under the transformation
. It is shown that the
magnetic solution obtained with the help of the procedure used in
Ref.~\cite{Cataldo}, can be obtained from the static BTZ solution using an
appropriate transformation. Superpositions of a perfect fluid and an electric
or a magnetic field are separately studied and their corresponding solutions
found.Comment: 8 pages, LaTeX, no figures, to appear in Physical Review
Multimode model for an atomic Bose-Einstein condensate in a ring-shaped optical lattice
We study the population dynamics of a ring-shaped optical lattice with a high
number of particles per site and a low, below ten, number of wells. Using a
localized on-site basis defined in terms of stationary states, we were able to
construct a multiple-mode model depending on relevant hopping and on-site
energy parameters. We show that in case of two wells, our model corresponds
exactly to the latest improvement of the two-mode model. We derive a formula
for the self-trapping period, which turns out to be chiefly ruled by the
on-site interaction energy parameter. By comparing to time dependent
Gross-Pitaevskii simulations, we show that the multimode model results can be
enhanced in a remarkable way over all the regimes by only renormalizing such a
parameter. Finally, using a different approach which involves only the ground
state density, we derive an effective interaction energy parameter that shows
to be in accordance with the renormalized one.Comment: 18 pages, 12 figure
Memory effects in superfluid vortex dynamics
The dissipative dynamics of a vortex line in a superfluid is investigated
within the frame of a non-Markovian quantal Brownian motion model. Our starting
point is a recently proposed interaction Hamiltonian between the vortex and the
superfluid quasiparticle excitations, which is generalized to incorporate the
effect of scattering from fermion impurities (He atoms). Thus, a
non-Markovian equation of motion for the mean value of the vortex position
operator is derived within a weak-coupling approximation. Such an equation is
shown to yield, in the Markovian and elastic scattering limits, a He
contribution to the longitudinal friction coefficient equivalent to that
arising from the Rayfield-Reif formula. Simultaneous Markov and elastic
scattering limits are found, however, to be incompatible, since an unexpected
breakdown of the Markovian approximation is detected at low cyclotron
frequencies. Then, a non-Markovian expression for the longitudinal friction
coefficient is derived and computed as a function of temperature and He
concentration. Such calculations show that cyclotron frequencies within the
range 0.010.03 ps yield a very good agreement to the longitudinal
friction figures computed from the Iordanskii and Rayfield-Reif formulas for
pure He, up to temperatures near 1 K. A similar performance is found for
nonvanishing He concentrations, where the comparison is also shown to be
very favorable with respect to the available experimental data. Memory effects
are shown to be weak and increasing with temperature and concentration.Comment: Incidence of radiation damping analyzed in Sections I and IV C (2
references added). Derivation of the vortex equation of motion moved to an
appendix; other minor changes about style and presentation. 13 pages, no
figures. Accepted for publication in the Journal of Low Temperature Physic
Dynamics in asymmetric double-well condensates
The dynamics of Bose-Einstein condensates in asymmetric double-wells is
studied. We construct a two-mode model and analyze the properties of the
corresponding phase-space diagram, showing in particular that the minimum of
the phase-space portrait becomes shifted from the origin as a consequence of
the nonvanishing overlap between the ground and excited states from which the
localized states are derived. We further incorporate effective interaction
corrections in the set of two-mode model parameters. Such a formalism is
applied to a recent experimentally explored system, which is confined by a
toroidal trap with radial barriers forming an arbitrary angle between them. We
confront the model results with Gross-Pitaevskii simulations for various angle
values finding a very good agreement. We also analyze the accuracy of a
previously employed simple model for moving barriers, exploring a possible
improvement that could cover a wider range of trap asymmetries.Comment: 15 pages, 11 figure
Dark soliton collisions in a toroidal Bose-Einstein condensate
We study the dynamics of two gray solitons in a Bose-Einstein condensate
confined by a toroidal trap with a tight confinement in the radial direction.
Gross-Pitaevskii simulations show that solitons can be long living objects
passing through many collisional processes. We have observed quite different
behaviors depending on the soliton velocity. Very slow solitons, obtained by
perturbing the stationary solitonic profile, move with a constant angular
velocity until they collide elastically and move in the opposite direction
without showing any sign of lowering their energy. In this case the density
notches are always well separated and the fronts are sharp and straight. Faster
solitons present vortices around the notches, which play a central role during
the collisions. We have found that in these processes the solitons lose energy,
as the outgoing velocity turns out to be larger than the incoming one. To study
the dynamics, we model the gray soliton state with a free parameter that is
related to the soliton velocity. We further analyze the energy, soliton
velocity and turning points in terms of such a free parameter, finding that the
main features are in accordance with the infinite one-dimensional system.Comment: 15 pages, 11 figures. Accepted in PR
Two-mode effective interaction in a double-well condensate
We investigate the origin of a disagreement between the two-mode model and
the exact Gross-Pitaevskii dynamics applied to double-well systems. In general
this model, even in its improved version, predicts a faster dynamics and
underestimates the critical population imbalance separating Josephson and
self-trapping regimes. We show that the source of this mismatch in the dynamics
lies in the value of the on-site interaction energy parameter. Using simplified
Thomas-Fermi densities, we find that the on-site energy parameter exhibits a
linear dependence on the population imbalance, which is also confirmed by
Gross-Pitaevskii simulations. When introducing this dependence in the two-mode
equations of motion, we obtain a reduced interaction energy parameter which
depends on the dimensionality of the system. The use of this new parameter
significantly heals the disagreement in the dynamics and also produces better
estimates of the critical imbalance.Comment: 5 pages, 4 figures, accepted in PR
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