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

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 $\omega$ and the wavenumber $q$ related by $\omega^2=Fq/m$. Here $F$ is the force due to the confining potential at the surface and $m$ is the particle mass. At shorter wavelengths we use a variational approach and find corrections to $\omega^2$ of order $q^4 \ln{q}$. 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.

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

To assess and be assessed: Upper secondary school students’ narratives of credibility judgements

Purpose – The purpose of this paper is to explore how students construct narratives of themselves as information seekers in a school context where their descriptions of their information activities are assessed and graded. Design/methodology/approach – Blog posts on credibility judgements written by 28 students at a Swedish upper secondary school were analysed through a bottom-up coding process based in the sociocultural concept of narratives of selves. Findings – Two tensions in the students’ accounts are identified. The first tension is that between the description of the individual, independent student and the description of the good group member. The second tension is between describing oneself as an independent information seeker and at the same time as someone who seeks information in ways that are sanctioned within the school setting. Research limitations/implications – The study focuses on a specific social practice and on situated activities, but also illustrates some aspects of information activities that pertain to educational contexts in general. It explores how social norms related to credibility judgements are expressed and negotiated in discursive interaction. Practical implications – The study highlights that when information activities become objects of assessment, careful consideration of what aspects are meant to be assessed is necessary. Originality/value – The study is based on the idea of information activities as socially and discursively shaped, and it illustrates some of the consequences when information activities become objects of teaching, learning, and grading

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

Vortices in Bose-Einstein-Condensed Atomic Clouds

The properties of vortex states in a Bose-Einstein condensed cloud of atoms are considered at zero temperature. Using both analytical and numerical methods we solve the time-dependent Gross-Pitaevskii equation for the case when a cloud of atoms containing a vortex is released from a trap. In two dimensions we find the simple result that the time dependence of the cloud radius is given by $(1+\omega^2t^2)^{1/2}$, where $\omega$ is the trap frequency. We calculate and compare the expansion of the vortex core and the cloud radius for different numbers of particles and interaction strengths, in both two and three dimensions, and discuss the circumstances under which vortex states may be observed experimentally.Comment: Revtex, 11 pages including 5 eps figures, submitted to Phys. Rev. A; new reference added, remark added in Sec. IIIB, axis label added in Fig.

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

Hydrodynamic Approach to Vortex Lifetime in Trapped Bose Condensates

We study a vortex in a two-dimensional, harmonically trapped Bose-Einstein condensate at zero temperature. Through a variational calculation using a trial condensate wave function and a nonlinear Schroedinger Lagrangian, we obtain the effective potential experienced by a vortex at an arbitrary position in the condensate, and find that an off-center vortex will move in a circular trajectory around the trap center. We find the frequency of this precession to be smaller than the elementary excitation frequencies in the cloud. We also study the radiation of sound from a moving vortex in an infinite, uniform system, and discuss the validity of this as an approximation for the trapped case. Furthermore, we estimate the lifetime of a vortex due to imperfections in the trapping potential.Comment: 10 pages, 1 eps figure, submitted to PRA, adjustments in response to referee, one refernce adde