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

Water system virus detection

The performance of a waste water reclamation system is monitored by introducing a non-pathogenic marker virus, bacteriophage F2, into the waste-water prior to treatment and, thereafter, testing the reclaimed water for the presence of the marker virus. A test sample is first concentrated by absorbing any marker virus onto a cellulose acetate filter in the presence of a trivalent cation at low pH and then flushing the filter with a limited quantity of a glycine buffer solution to desorb any marker virus present on the filter. Photo-optical detection of indirect passive immune agglutination by polystyrene beads indicates the performance of the water reclamation system in removing the marker virus. A closed system provides for concentrating any marker virus, initiating and monitoring the passive immune agglutination reaction, and then flushing the system to prepare for another sample

Water system virus detection

A monitoring system developed to test the capability of a water recovery system to reject the passage of viruses into the recovered water is described. A nonpathogenic marker virus, bacteriophage F2, is fed into the process stream before the recovery unit and the reclaimed water is assayed for its presence. Detection of the marker virus consists of two major components, concentration and isolation of the marker virus, and detection of the marker virus. The concentration system involves adsorption of virus to cellulose acetate filters in the presence of trivalent cations and low pH with subsequent desorption of the virus using volumes of high pH buffer. The detection of the virus is performed by a passive immune agglutination test utilizing specially prepared polystyrene particles. An engineering preliminary design was performed as a parallel effort to the laboratory development of the marker virus test system. Engineering schematics and drawings of a fully functional laboratory prototype capable of zero-G operation are presented. The instrument consists of reagent pump/metering system, reagent storage containers, a filter concentrator, an incubation/detector system, and an electronic readout and control system

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

Information requirements for supersonic transport operation Final report

Effects of meteorological parameters and instrument errors on vertical flight performance of supersonic transport

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

A Suggested Criterion for Selecting between E-V and Stochastic Dominance Analysis Tools

Research Methods/ Statistical Methods,