16,367 research outputs found
Extension of the Thomas-Fermi approximation for trapped Bose-Einstein condensates with an arbitrary number of atoms
By incorporating the zero-point energy contribution we derive simple and
accurate extensions of the usual Thomas-Fermi (TF) expressions for the
ground-state properties of trapped Bose-Einstein condensates that remain valid
for an arbitrary number of atoms in the mean-field regime. Specifically, we
obtain approximate analytical expressions for the ground-state properties of
spherical, cigar-shaped, and disk-shaped condensates that reduce to the correct
analytical formulas in both the TF and the perturbative regimes, and remain
valid and accurate in between these two limiting cases. Mean-field quasi-1D and
-2D condensates appear as simple particular cases of our formulation. The
validity of our results is corroborated by an independent numerical computation
based on the 3D Gross-Pitaevskii equation.Comment: 5 pages, 3 figures. Final version published in Phys. Rev.
Three-dimensional gap solitons in Bose-Einstein condensates supported by one-dimensional optical lattices
We study fundamental and compound gap solitons (GSs) of matter waves in
one-dimensional (1D) optical lattices (OLs) in a three-dimensional (3D)
weak-radial-confinement regime, which corresponds to realistic experimental
conditions in Bose-Einstein condensates (BECs). In this regime GSs exhibit
nontrivial radial structures. Associated with each 3D linear spectral band
exists a family of fundamental gap solitons that share a similar transverse
structure with the Bloch waves of the corresponding linear band. GSs with
embedded vorticity may exist \emph{inside} bands corresponding to other
values of . Stable GSs, both fundamental and compound ones (including vortex
solitons), are those which originate from the bands with lowest axial and
radial quantum numbers. These findings suggest a scenario for the experimental
generation of robust GSs in 3D settings.Comment: 5 pages, 5 figures; v2: matches published versio
Exploring singlet deflection of gauge mediation
We embed the Next-to Minimal Supersymmetric Standard Model into gauge
mediation of supersymmetry breaking and study the phenomenology of scenarios
where the gauge-mediation contributions to soft parameters are deflected by
superpotential interactions of the gauge singlet with the messenger fields and
the Higgs doublets. This kind of models provide a satisfactory solution to the
mu-b_mu problem of gauge mediation, compatible with the adequate pattern of
electroweak symmetry breaking and a realistic spectrum with supersymmetric
partners at the TeV scale without requiring a significant fine tuning.Comment: Latex 18 pages, 4 eps figures. Minor corrections, version published
in Phys. Rev.
Dynamical evolution of a doubly-quantized vortex imprinted in a Bose-Einstein Condensate
The recent experiment by Y. Shin \emph{et al.} [Phys. Rev. Lett. \textbf{93},
160406 (2004)] on the decay of a doubly quantized vortex imprinted in Na condensates is analyzed by numerically solving the Gross-Pitaevskii
equation. Our results, which are in very good quantitative agreement with the
experiment, demonstrate that the vortex decay is mainly a consequence of
dynamical instability. Despite apparent contradictions, the local density
approach is consistent with the experimental results. The monotonic increase
observed in the vortex lifetimes is a consequence of the fact that, for large
condensates, the measured lifetimes incorporate the time it takes for the
initial perturbation to reach the central slice. When considered locally, the
splitting occurs approximately at the same time in every condensate, regardless
of its size.Comment: 5 pages, 4 figure
Effective mean-field equations for cigar-shaped and disk-shaped Bose-Einstein condensates
By applying the standard adiabatic approximation and using the accurate
analytical expression for the corresponding local chemical potential obtained
in our previous work [Phys. Rev. A \textbf{75}, 063610 (2007)] we derive an
effective 1D equation that governs the axial dynamics of mean-field
cigar-shaped condensates with repulsive interatomic interactions, accounting
accurately for the contribution from the transverse degrees of freedom. This
equation, which is more simple than previous proposals, is also more accurate.
Moreover, it allows treating condensates containing an axisymmetric vortex with
no additional cost. Our effective equation also has the correct limit in both
the quasi-1D mean-field regime and the Thomas-Fermi regime and permits one to
derive fully analytical expressions for ground-state properties such as the
chemical potential, axial length, axial density profile, and local sound
velocity. These analytical expressions remain valid and accurate in between the
above two extreme regimes. Following the same procedure we also derive an
effective 2D equation that governs the transverse dynamics of mean-field
disk-shaped condensates. This equation, which also has the correct limit in
both the quasi-2D and the Thomas-Fermi regime, is again more simple and
accurate than previous proposals. We have checked the validity of our equations
by numerically solving the full 3D Gross-Pitaevskii equation.Comment: 11 pages, 7 figures; Final version published in Phys. Rev. A;
Manuscript put in the archive and submitted to Phys. Rev. A on 17 July 200
Quantum Renormalization Group for 1 Dimensional Fermion Systems
Inspired by the superblock method of White, we introduce a simple
modification of the standard Renormalization Group (RG) technique for the study
of quantum lattice systems. Our method which takes into account the effect of
Boundary Conditions(BC), may be regarded as a simple way for obtaining first
estimates of many properties of quantum lattice systems. By applying this
method to the 1-dimensional free and interacting fermion system, we obtain the
ground state energy with much higher accuracy than the standard RG. We also
calculate the density-density correlation function in the free-fermion case
which shows good agreement with the exact result.Comment: LaTex file, 1 PS figur
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