Bethe Ansatz Solutions of the Bose-Hubbard Dimer

The Bose-Hubbard dimer Hamiltonian is a simple yet effective model for describing tunneling phenomena of Bose-Einstein condensates. One of the significant mathematical properties of the model is that it can be exactly solved by Bethe ansatz methods. Here we review the known exact solutions, highlighting the contributions of V.B. Kuznetsov to this field. Two of the exact solutions arise in the context of the Quantum Inverse Scattering Method, while the third solution uses a differential operator realisation of the su(2) Lie algebra.Comment: This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Integrable coupling in a model for Josephson tunneling between non-identical BCS systems

We extend a recent construction for an integrable model describing Josephson tunneling between identical BCS systems to the case where the BCS systems have different single particle energy levels. The exact solution of the generalized model is obtained through the Bethe ansatz.Comment: 8 pages, latex, to appear in edition of Int. J. Mod. Phys. B commemorating the 70th birthday of F.Y. W

Some spectral equivalences between Schrodinger operators

Spectral equivalences of the quasi-exactly solvable sectors of two classes of Schrodinger operators are established, using Gaudin-type Bethe ansatz equations. In some instances the results can be extended leading to full isospectrality. In this manner we obtain equivalences between PT-symmetric problems and Hermitian problems. We also find equivalences between some classes of Hermitian operators.Comment: 14 page

MELEES - e-support or mayhem?

This paper reports on progress in developing a web-based environment to support non-specialist mathematics students taking University level Mathematics as a compulsory subject in their first and second years. The scale and diversity of the service teaching provision at Nottingham invites the use of a technology-based framework in order to make available the ‘good practice’ features developed both locally and elsewhere. Initially the two year development is focusing on: • establishing a supportive environment; • providing feedback to students, their lecturers and importantly to their home Schools; • identifying and supporting e-learning strategies; • improving student motivation. Current activities have been primarily directed to the first three bullet points

Principles of Geology and sensory experience at London's Cyclorama

The Cyclorama opened in London in 1848 with a representation of the 1755 Lisbon earthquake that reportedly terrified audiences with its realistic aural and visual effects. During the first half of the century Londoners had been confronted with a rapid succession of revolutions in scientific thought, which needed to be assimilated into the emotional as well as the intellectual structures of public life. The geologist Charles Lyell had recently explained earthquakes and volcanic activity in a manner that fundamentally changed public understanding of the history of the earth, and in so doing challenged the religious narratives that had formerly underpinnedit. The Cyclorama invited the spectator to confront such destruction in this new light: the frighteningly immersive visual and aural effects and the comforting narratives offered by accompanying musical excerpts (from works by Auber, Beethoven, and Rossini) were crucial to the shaping of the experience, and can be understood in the context of other artistic and poetic responses to Lyell’s proposals. The music helped to articulate something of the competing perspectives on the crisis of faith that was exercising the intelligentsia at mid-century and offered a conduit for both emotional and intellectual responses

Combating falsified medicines in Africa through digital artefacts

Falsified medicines are again in the news, this time in a piece for the BBC News’ websites business section. In his article, Matthew Wall looks at the problem of combating falsified, counterfeit and substandard anti-malarial medicines in Africa through the use of alternative technologies for tracking the identity of the medicines’ original pack – the original pack being the box of 14 or 28 tablets received for the patient

Hub and spoke dispensing: safety and sociotechnical pliability

Over the course of the last year, the Department of Health has looked at the use of hub and spoke dispensing systems for community pharmacy in England, a technology which some view as an inevitable extension of electronic prescription transmission in primary care. In a hub and spoke system, medicines required for a primary care prescription are put together at a remotely located warehouse and then transported to a spoke site, such as a community pharmacy, where they can be collected by the patient. The economies of scale that such a model offers support the use of robotic dispensing