Quantum Mechanics and the Metrics of General Relativity

A one-to-one correspondence is established between linearized space-time metrics of general relativity and the wave equations of quantum mechanics. Also, the key role of boundary conditions in distinguishing quantum mechanics from classical mechanics will emerge naturally from the procedure. Finally, we will find that the methodology will enable us to introduce not only test charges but also test masses by means of gauges.Comment: 24 pages, to be published in Foundation of Physics (IARD proc.

Effective Lagrangian of unitary Fermi gas from ε\varepsilon expansion

Using $\varepsilon$ expansion technique proposed in \cite{Nishida:2006br} we derive an effective Lagrangian (Ginzburg-Landau-like functional) of the degenerate unitary Fermi gas to the next-to-leading (NLO) order in $\varepsilon.$ It is demonstrated that for many realistic situations it is sufficient to retain leading order (LO) terms in the derivative expansion. The functional is used to study vortex structure in the symmetric gas, and interface between normal and superfluid phases in the polarized gas. The resulting surface free energy is about four times larger than the value previously quoted in the literature.Comment: 17 pages, 4 figure

Stiff knots

We report on the geometry and mechanics of knotted stiff strings. We discuss both closed and open knots. Our two main results are: (i) Their equilibrium energy as well as the equilibrium tension for open knots depend on the type of knot as the square of the bridge number; (ii) Braid localization is found to be a general feature of stiff strings entanglements, while angles and knot localization are forbidden. Moreover, we identify a family of knots for which the equilibrium shape is a circular braid. Two other equilibrium shapes are found from Monte Carlo simulations. These three shapes are confirmed by rudimentary experiments. Our approach is also extended to the problem of the minimization of the length of a knotted string with a maximum allowed curvature.Comment: Submitted to Phys. Rev.

Evaluation and decentralised governance: Examples of inspections in polycentric education systems

Across Europe schools and other service providers increasingly operate in networks to provide inclusive education or develop and implement more localized school-to-school improvement models. As some education systems move towards more decentralized decision-making where multiple actors have an active role in steering and governing schools, the tasks and responsibilities of Inspectorates of Education must also change. This paper reflects on these changes and suggests ‘polycentric’ inspection models that fit such a decentralized context. Examples of inspection frameworks and methods from Northern Ireland, England and the Netherlands are provided, as well as a brief discussion of the potential impact of such ‘polycentric’ models

3D modelling of upwelling around a headland

Hydrodynamic

‘Subjects and Objects: Material Expressions of Love and Loyalty in Seventeenth-Century England’, in special section on ‘Loyalties and Allegiances in Early Modern England’ in Journal of British Studies Vol. 48: 4 (October, 2009)

This article investigates how and where the emotive relations between subject and state were forged and how these ideas were manifested in early modern England. McShane describes an affective economy of loyalty, embodied in cheap and accessible political commodities: decorated objects made of clay, metals, and paper, on which precious household resources of time, money and emotion were spent. She argues that by engendering, inculcating and insinuating codes of political love into people’s ‘emotional, sensual, representational, and communicative’ lives, ‘loyal’ goods acted as vehicles and texts for what Victoria Kahn describes as ‘the supplementary role of the passions’ in ‘forging political obligation’ and the reformulation of ‘the duty to love’ of both subject and king in 17th-century England. McShane’s research contributes to a growing theme in scholarship, namely the active consumption of politically significant goods. This essay extends the range of objects under examination to include quotidian household items, shedding light on the dissemination and construction of early modern loyalty across a much wider social scale. The research draws on an extensive survey of collections held at the V&A, the Museum of London, Ashmolean Museum, Fitzwilliam Museum and Burrell Collection. Importantly, by putting illustrated print products back together with other political commodities in the early modern home, creating a broad archive of objects and text-objects where each informs the other, McShane’s approach challenges the typical social historical methodology, which uses material culture as merely illustrative of textual sources. This article was part of a special section on loyalty and allegiance in early modern England, co-edited by McShane with Dr Ted Vallance for one of the leading scholarly journals in the field. The material was drawn from a workshop on the topic held at the University of Liverpool funded by the British Academy, University of Liverpool and the Scouloudi Foundation (2007)

Characterization of elastic scattering near a Feshbach resonance in rubidium 87

The s-wave scattering length for elastic collisions between 87Rb atoms in the state |f,m_f>=|1,1> is measured in the vicinity of a Feshbach resonance near 1007 G. Experimentally, the scattering length is determined from the mean-field driven expansion of a Bose-Einstein condensate in a homogeneous magnetic field. The scattering length is measured as a function of the magnetic field and agrees with the theoretical expectation. The position and the width of the resonance are determined to be 1007.40 G and 0.20 G, respectively.Comment: 4 pages, 2 figures minor revisions: added Ref.6, included error bar

Spectroscopic Temperature Determination of Degenerate Fermi Gases

We suggest a simple method for measuring the temperature of ultra-cold gases made of fermions. We show that by using a two-photon Raman probe, it is possible to obtain lineshapes which reveal properties of the degenerate sample, notably its temperature $T$. The proposed method could be used with identical fermions in different hyperfine states interacting via s-wave scattering or identical fermions in the same hyperfine state via p-wave scattering. We illustrate the applicability of the method in realistic conditions for $^6$Li prepared in two different hyperfine states. We find that temperatures down to 0.05 $T_{F}$ can be determined by this {\it in-situ} method.Comment: 7 pages, 4 figures, Revtex