Breathing SPACE – a practical approach to the breathless patient.

Breathlessness is a common symptom which may have multiple causes in any one individual and causes which may change over time. Breathlessness campaigns encourage people to see their GP if they are unduly breathless. Members of the London Respiratory Network collaborated to develop a tool which would encourage a holistic approach to breathlessness, which was applicable both at the time of diagnosis and during ongoing management. This has led to the development of the aide memoire “Breathing SPACE” which encompasses 5 key themes – Smoking, Pulmonary disease, Anxiety/psychosocial factors, Cardiac disease and Exercise/fitness. A particular concern was to ensure that high value interventions (smoking cessation and exercise interventions) are prioritised across the life-course and throughout the course of disease management. The approach is relevant both to well people and in those with an underling diagnosis or diagnoses. The inclusion of anxiety draws attention to the importance of mental health issues. Parity of esteem requires the physical health problems of people with mental illness to be addressed. The SPACE mnemonic also addresses the problem of underdiagnosis of heart disease in people with lung disease and vice versa, as well as the systematic undertreatment of these conditions where they do co-occur

Exact results for the one-dimensional many-body problem with contact interaction: Including a tunable impurity

The one-dimensional problem of $N$ particles with contact interaction in the presence of a tunable transmitting and reflecting impurity is investigated along the lines of the coordinate Bethe ansatz. As a result, the system is shown to be exactly solvable by determining the eigenfunctions and the energy spectrum. The latter is given by the solutions of the Bethe ansatz equations which we establish for different boundary conditions in the presence of the impurity. These impurity Bethe equations contain as special cases well-known Bethe equations for systems on the half-line. We briefly study them on their own through the toy-examples of one and two particles. It turns out that the impurity can be tuned to lift degeneracies in the energies and can create bound states when it is sufficiently attractive. The example of an impurity sitting at the center of a box and breaking parity invariance shows that such an impurity can be used to confine asymmetrically a stationary state. This could have interesting applications in condensed matter physics.Comment: 20 pages, 5 figures, version accepted for publication: some typos corrected, references and comments adde

The challenge of the chiral Potts model

The chiral Potts model continues to pose particular challenges in statistical mechanics: it is ``exactly solvable'' in the sense that it satisfies the Yang-Baxter relation, but actually obtaining the solution is not easy. Its free energy was calculated in 1988 and the order parameter was conjectured in full generality a year later. However, a derivation of that conjecture had to wait until 2005. Here we discuss that derivation.Comment: 22 pages, 3 figures, 29 reference

Eigenvectors of Baxter-Bazhanov-Stroganov \tau^{(2)}(t_q) model with fixed-spin boundary conditions

The aim of this contribution is to give the explicit formulas for the eigenvectors of the transfer-matrix of Baxter-Bazhanov-Stroganov (BBS) model (N-state spin model) with fixed-spin boundary conditions. These formulas are obtained by a limiting procedure from the formulas for the eigenvectors of periodic BBS model. The latter formulas were derived in the framework of the Sklyanin's method of separation of variables. In the case of fixed-spin boundaries the corresponding T-Q Baxter equations for the functions of separated variables are solved explicitly. As a particular case we obtain the eigenvectors of the Hamiltonian of Ising-like Z_N quantum chain model.Comment: 14 pages, paper submitted to Proceedings of the International Workshop "Classical and Quantum Integrable Systems" (Dubna, January, 2007