19,002 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.

### On the lattice of subgroups of a free group: complements and rank

A $\vee$-complement of a subgroup $H \leqslant \mathbb{F}_n$ is a subgroup $K
\leqslant \mathbb{F}_n$ such that $H \vee K = \mathbb{F}_n$. If we also ask $K$
to have trivial intersection with $H$, then we say that $K$ is a
$\oplus$-complement of $H$. The minimum possible rank of a $\vee$-complement
(resp. $\oplus$-complement) of $H$ is called the $\vee$-corank (resp.
$\oplus$-corank) of $H$. We use Stallings automata to study these notions and
the relations between them. In particular, we characterize when complements
exist, compute the $\vee$-corank, and provide language-theoretical descriptions
of the sets of cyclic complements. Finally, we prove that the two notions of
corank coincide on subgroups that admit cyclic complements of both kinds.Comment: 27 pages, 5 figure

### USHER: an algorithm for particle insertion in dense fluids

The insertion of solvent particles in molecular dynamics simulations of
complex fluids is required in many situations involving open systems, but this
challenging task has been scarcely explored in the literature. We propose a
simple and fast algorithm (USHER) that inserts the new solvent particles at
locations where the potential energy has the desired prespecified value. For
instance, this value may be set equal to the system's excess energy per
particle, in such way that the inserted particles are energetically
indistinguishable from the other particles present. During the search for the
insertion site, the USHER algorithm uses a steepest descent iterator with a
displacement whose magnitude is adapted to the local features of the energy
landscape. The only adjustable parameter in the algorithm is the maximum
displacement and we show that its optimal value can be extracted from an
analysis of the structure of the potential energy landscape. We present
insertion tests in periodic and non-periodic systems filled with a
Lennard-Jones fluid whose density ranges from moderate values to high values.Comment: 10 pages (Latex), 8 figures (postscript); J. Chem. Phys. (in press)
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### 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.

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