Random matrices and quantum spin chains

Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the density of states when $n \rightarrow\infty$, giving explicit bounds on the rate of approach to the limit. Universality within a class of probability measures and the extension to more general interaction geometries are established. The level spacing distributions of the Gaussian Orthogonal, Unitary and Symplectic Ensembles are observed numerically for the energy levels in these ensembles.Comment: Updated figures, as accepted in 'Markov Processes and Related Fields' on 3 March 201

Spectra and eigenstates of spin chain Hamiltonians

We prove that translationally invariant Hamiltonians of a chain of $n$ qubits with nearest-neighbour interactions have two seemingly contradictory features. Firstly in the limit $n\rightarrow\infty$ we show that any translationally invariant Hamiltonian of a chain of $n$ qubits has an eigenbasis such that almost all eigenstates have maximal entanglement between fixed-size sub-blocks of qubits and the rest of the system; in this sense these eigenstates are like those of completely general Hamiltonians (i.e. Hamiltonians with interactions of all orders between arbitrary groups of qubits). Secondly in the limit $n\rightarrow\infty$ we show that any nearest-neighbour Hamiltonian of a chain of $n$ qubits has a Gaussian density of states; thus as far as the eigenvalues are concerned the system is like a non-interacting one. The comparison applies to chains of qubits with translationally invariant nearest-neighbour interactions, but we show that it is extendible to much more general systems (both in terms of the local dimension and the geometry of interaction). Numerical evidence is also presented which suggests that the translational invariance condition may be dropped in the case of nearest-neighbour chains.Comment: Updated figures, as accepted in 'Communications in Mathematical Physics' on 5 January 201

Quantised vortices and mutual friction in relativistic superfluids

We consider the detailed dynamics of an array of quantised superfluid vortices in the framework of general relativity, as required for quantitative modelling of realistic neutron star cores. Our model builds on the variational approach to relativistic (multi-) fluid dynamics, where the vorticity plays a central role. The description provides a natural extension of, and as it happens a better insight into, existing Newtonian models. In particular, we account for the mutual friction associated with scattering of a second "normal" component in the mixture off of the superfluid vortices.Comment: 9 pages, RevTe

Olfactory variation in mouse husbandry and its implications for refinement and standardisation: UK survey of non-animal scents

With their highly sensitive olfactory system, the behaviour and physiology of mice are not only influenced by the scents of conspecifics and other species, but also by many other chemicals in the environment. The constraints of laboratory housing limit a mouse’s capacity to avoid aversive odours that could be present in the environment. Potentially odorous items routinely used for husbandry procedures, such as sanitizing products and gloves, could be perceived by mice as aversive or attractive, and affect their behaviour, physiology and experimental results. A survey was sent to research institutions in the UK to enquire about husbandry practices that could impact on the olfactory environment of the mouse. Responses were obtained from 80 individuals working in 51 institutions. Husbandry practices varied considerably. Seventy percent of respondents reported always wearing gloves for handling mice, with nitrile being the most common glove material (94%) followed by latex (23%) and vinyl (14%). Over six different products were listed for cleaning surfaces, floors, anaesthesia and euthanasia chambers and behavioural apparatus. In all cases Trigene™ (now called Anistel™) was the most common cleaning product used (43, 41, 40 and 49%, respectively). Depending on the attribute considered, between 7 and 19% of respondents thought that cleaning products definitely, or were likely to, have strong effects on standardization, mouse health, physiology or behaviour. Understanding whether and how these odours affect mouse welfare will help to refine mouse husbandry and experimental procedures through practical recommendations, to improve the quality of life of laboratory animals and the experimental data obtained

Performance analysis practice within Olympic and Paralympic sports: a comparison of coach and analyst experiences

Concordance between 18 coaches (mean performance analysis experience: 8.3 ± 4.8 years) and 23 performance analysts (mean: 6.4 ± 4.1 years) regarding their performance analysis delivery within applied Olympic and Paralympic environments was investigated using survey-based methods. There was clear agreement on the provision, importance and need for full video. The majority of analysts (73.9%) provided profiling often or all of the time, whereas only one third of coaches felt that this was the required amount. Coaches not only agreed that coaching philosophy was the main factor directing analysis but also emphasised that training goals, level or age of athlete and discussions with athletes were influencers, far more than the analysts realised. A potential barrier for better communication was time, highlighted by all analysts as a major factor impacting their role. The majority of analysts (87%) attempted to provide feedback to athletes within one hour of performance, often or all the time. Coaches expressed a similar philosophy but were far more likely to want to provide feedback at later times. These findings should be utilised by analysts and coaches to review practice, identify gaps within practice and highlight areas for development

Holomorphic selection rules, the origin of the mu term, and thermal inflation

When an abelian gauge theory with integer charges is spontaneously broken by the expectation value of a charge Q field, there remains a Z_Q discrete symmetry. In a supersymmetric theory, holomorphy adds additional constraints on the operators that can appear in the effective superpotential. As a result, operators with the same mass dimension but opposite sign charges can have very different coupling strengths. In the present work we characterize the operator hierarchies in the effective theory due to holomorphy, and show that there exist simple relationships between the size of an operator and its mass dimension and charge. Using such holomorphy-induced operator hierarchies, we construct a simple model with a naturally small supersymmetric mu term. This model also provides a concrete realization of late-time thermal inflation, which has the ability to solve the gravitino and moduli problems of weak-scale supersymmetry.Comment: 18 pages, 1 figur

Elite coaches’ use and engagement with performance analysis within Olympic and Paralympic sport

The use and implementation of performance analysis and feedback by 18 elite Olympic/Paralympic coaches (coaching experience 16.1 ± 7.4; experience using performance analysis 8.3 ± 4.8 years) was explored via an online questionnaire (mean time to complete = 29 minutes). Likert scales were used to facilitate cross-sport comparison. Comment boxes were included to enable additional information to be provided if deemed necessary. Training goals, athlete discussion and coaching philosophy were the most prominent features influencing analysis direction. Time available had the greatest impact upon feedback provision. The main analysis techniques used were video, performance reports, and trend analysis. Coaches with greater experience delivered significantly more feedback sessions within 1-hour of performance. Feedback sessions were < 20-minutes in duration and delivered in a balanced (experienced) or mostly positive (inexperienced) approach. Feedback was delivered consistently according to a preferred schedule, face-to-face, and within an individual format. Sessions were usually coach led, however considerable value in a combined or analyst led approach was demonstrated. The findings have begun to illustrate practice within elite sport from the perspective of a key user of performance analysis, i.e. the coach, and have clear implications for practitioners by identifying the key areas coaches’ value from performance analysis

The implementation of performance analysis and feedback within Olympic sport: the performance analyst’s perspective

The study considered performance analysis and feedback from the perspective of the performance analyst through the investigation of the ‘what’, ‘how’, and ‘when’ of practice within a selection of Olympic sports. Twenty-three performance analysts (experience 6.4 ± 4.1 years) engaged in a structured interview (85 ± 15 minutes) regarding their processes within applied practice. Likert scales (All the time, Often, Sometimes, Rarely, Never) were used to facilitate cross sport and environment comparison. The performance analysts highlighted the experience of their coaches as the most prominent feature influencing analysis direction and time had the greatest impact upon feedback provision. The main analysis techniques used were video, profiling and performance reports. Feedback was delivered primarily either, 1) < 1-hour post-performance within sessions lasting < 10-minutes or 2) the following day within sessions lasting 25+ minutes. Video feedback was usually coach led, however data delivery was more evenly distributed between coach and analyst. Very similar processes across the participants were identified, despite a wide variety of sports and participant experience levels. The findings have begun to illustrate practice within elite sport whilst highlighting the importance and need for further practitioner-based investigation regarding the use of performance analysis and feedback within applied context

Expressive and scalable finite element simulation beyond 1000 cores

http://www.hector.ac.uk/cse/distributedcse/reports/UniDOLFIN/The FEniCS Project is a widely used, open-source problem solving environment for partial differential equations that allows users to specify equations in mathematical symbolic form via a domain-specific language, and solve them using the finite element method. The FEniCS Problem solving environment provides C++ and Python interfaces, and relies on automated code generation to reconcile expressive input with high performance. Because of the generic nature of the software, many different scientific problems are being addressed using FEniCS/DOLFIN, including geodynamics, heat flow, elasticity, electromagnetics, flow in porous media, Navier--Stokes equations and acoustics. The key aims of this project were to enhance the applicability and usability of DOLFIN, the core finite element library in the FEniCS Project, on parallel architectures. DOLFIN already supported fully distributed computation via MPI, but lacked some important infrastructure for enabling large scale parallel computation. This included a lack of (i) scalable parallel I/O and (ii) parallel mesh refinement. In addition, (iii) DOLFIN did not support threaded operations in combination with MPI. Implementation of the three aforementioned points formed the objectives of this project. All three objectives have been realised and exceeded, and the computer code developed is publicly available. Outcomes of this project are either already in a release of DOLFIN or are in development repositories and will be included in the next release, and are already being used in a number of research projects, including projects supported by UK research councils.This project was funded under the HECToR Distributed Computational Science and Engineering (CSE) Service operated by NAG Ltd. HECToR - A Research Councils UK High End Computing Service - is the UK's national supercomputing service, managed by EPSRC on behalf of the participating Research Councils. Its mission is to support capability science and engineering in UK academia. The HECToR supercomputers are managed by UoE HPCx Ltd and the CSE Support Service is provided by NAG Ltd