893 research outputs found
Construction of a giant vortex state in a trapped Fermi system
A superfluid atomic Fermi system may support a giant vortex if the trapping
potential is anharmonic. In such a potential, the single-particle spectrum has
a positive curvature as a function of angular momentum. A tractable model is
put up in which the lowest and next lowest Landau levels are occupied.
Different parameter regimes are identified and characterized. Due to the
dependence of the interaction on angular momentum quantum number, the Cooper
pairing is at its strongest not only close to the Fermi level, but also close
to the energy minimum. It is shown that the gas is superfluid in the interior
of the toroidal density distribution and normal in the outer regions.
Furthermore, the pairing may give rise to a localized density depression in
configuration space.Comment: 12 pages, 14 figure file
Rotating states for trapped bosons in an optical lattice
Rotational states for trapped bosons in an optical lattice are studied in the
framework of the Hubbard model. Critical frequencies are calculated and the
main parameter regimes are identified. Transitions are observed from edge
superfluids to vortex lattices with Mott insulating cores, and subsequently to
lattices of interstitial vortices. The former transition coincides with the
Mott transition. Changes in symmetry of the vortex lattices are observed as a
function of lattice depth. Predictions for experimental signatures are
presented.Comment: 6 pages, 6 figures, accepted for publication in EP
Stability of the solutions of the Gross-Pitaevskii equation
We examine the static and dynamic stability of the solutions of the
Gross-Pitaevskii equation and demonstrate the intimate connection between them.
All salient features related to dynamic stability are reflected systematically
in static properties. We find, for example, the obvious result that static
stability always implies dynamic stability and present a simple explanation of
the fact that dynamic stability can exist even in the presence of static
instability.Comment: 7 pages, 1 figur
The Surface of a Bose-Einstein Condensed Atomic Cloud
We investigate the structure and collective modes of a planar surface of a
trapped Bose-Einstein condensed gas at zero temperature. In the long-wavelength
limit we find a mode similar to the gravity wave on the surface of a fluid with
the frequency and the wavenumber related by . Here
is the force due to the confining potential at the surface and is the
particle mass. At shorter wavelengths we use a variational approach and find
corrections to of order . We demonstrate the usefulness
of the concept of an effective surface tension for describing both static and
dynamic properties of condensed atomic clouds.Comment: 8 pages, REVTEX, submitted to Phys. Rev.
Dipole and monopole modes in the Bose-Hubbard model in a trap
The lowest-lying collective modes of a trapped Bose gas in an optical lattice
are studied in the Bose-Hubbard model. An exact diagonalization of the
Hamiltonian is performed in a one-dimensional five-particle system in order to
find the lowest few eigenstates. Dipole and breathing character of the
eigenstates is confirmed in the limit where the tunneling dominates the
dynamics, but under Mott-like conditions the excitations do not correspond to
oscillatory modes.Comment: 19 pages, 11 figures; submitted to Phys. Rev.
Center of mass rotation and vortices in an attractive Bose gas
The rotational properties of an attractively interacting Bose gas are studied
using analytical and numerical methods. We study perturbatively the ground
state phase space for weak interactions, and find that in an anharmonic trap
the rotational ground states are vortex or center of mass rotational states;
the crossover line separating these two phases is calculated. We further show
that the Gross-Pitaevskii equation is a valid description of such a gas in the
rotating frame and calculate numerically the phase space structure using this
equation. It is found that the transition between vortex and center of mass
rotation is gradual; furthermore the perturbative approach is valid only in an
exceedingly small portion of phase space. We also present an intuitive picture
of the physics involved in terms of correlated successive measurements for the
center of mass state.Comment: version2, 17 pages, 5 figures (3 eps and 2 jpg
Dynamical stability of a doubly quantized vortex in a three-dimensional condensate
The Bogoliubov equations are solved for a three-dimensional Bose-Einstein
condensate containing a doubly quantized vortex, trapped in a harmonic
potential. Complex frequencies, signifying dynamical instability, are found for
certain ranges of parameter values. The existence of alternating windows of
stability and instability, respectively, is explained qualitatively and
quantitatively using variational calculus and direct numerical solution. It is
seen that the windows of stability are much smaller for a cigar shaped
condensate than for a pancake shaped one, which is consistent with the findings
of recent experiments.Comment: 23 pages, 11 figure
Automating Security Analysis: Symbolic Equivalence of Constraint Systems
We consider security properties of cryptographic protocols, that are either trace properties (such as confidentiality or authenticity) or equivalence properties (such as anonymity or strong secrecy). Infinite sets of possible traces are symbolically represented using deducibility constraints. We give a new algorithm that decides the trace equivalence for the traces that are represented using such constraints, in the case of signatures, symmetric and asymmetric encryptions. Our algorithm is implemented and performs well on typical benchmarks. This is the first implemented algorithm, deciding symbolic trace equivalence
Correlations and superfluidity of a one-dimensional Bose gas in a quasiperiodic potential
We consider the correlations and superfluid properties of a Bose gas in an
external potential. Using a Bogoliubov scheme, we obtain expressions for the
correlation function and the superfluid density in an arbitrary external
potential. These expressions are applied to a one-dimensional system at zero
temperature subject to a quasiperiodic modulation. The critical parameters for
the Bose glass transition are obtained using two different criteria and the
results are compared. The Lifshits glass is seen to be the limiting case for
vanishing interactions.Comment: Published in PRA, typos correcte
Information Research
Introduction. This study explored how various meanings are attributed to the term facts in Swedish schools and how this may shape conditions for students' learning. The understanding of information activities as social, communicative, and discursive, which motivates the study, is informed by a sociocultural perspective of learning and information interaction. Method. The study re-analyses empirical data from four previous research projects, where material was collected through various qualitative methods, mainly interviews, observations, and document analysis. The material involved 14 classes from year 2 to year 12.Analysis. The data were analysed thematically. In the material, 565 occurrences of facts are identified and categorised. Results. The analysis generated three themes. Firstly, facts were associated with specific genres or modalities. Secondly, facts were seen as distinguishable, external, and tangible. Thirdly, facts came across as having strong connections to neutrality and they were viewed as evidence. Conclusions. The analysis showed variation in how the study participants talked about facts. Despite the dominant associations, each theme displayed more complex meanings of the term, which indicates that fact cannot be equated to how the term has been used as an analytical term in previous research. The frequent use of the term facts can be understood as a result of the strong focus on students seeking and using certain types of information for writing school reports. The results show how important it is that information researchers adopt an open and explorative approach to the meaning of the language used in school activities that they study
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