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

Musculoskeletal Geometry, Muscle Architecture and Functional Specialisations of the Mouse Hindlimb

Mice are one of the most commonly used laboratory animals, with an extensive array of disease models in existence, including for many neuromuscular diseases. The hindlimb is of particular interest due to several close muscle analogues/homologues to humans and other species. A detailed anatomical study describing the adult morphology is lacking, however. This study describes in detail the musculoskeletal geometry and skeletal muscle architecture of the mouse hindlimb and pelvis, determining the extent to which the muscles are adapted for their function, as inferred from their architecture. Using I2KI enhanced microCT scanning and digital segmentation, it was possible to identify 39 distinct muscles of the hindlimb and pelvis belonging to nine functional groups. The architecture of each of these muscles was determined through microdissections, revealing strong architectural specialisations between the functional groups. The hip extensors and hip adductors showed significantly stronger adaptations towards high contraction velocities and joint control relative to the distal functional groups, which exhibited larger physiological cross sectional areas and longer tendons, adaptations for high force output and elastic energy savings. These results suggest that a proximo-distal gradient in muscle architecture exists in the mouse hindlimb. Such a gradient has been purported to function in aiding locomotor stability and efficiency. The data presented here will be especially valuable to any research with a focus on the architecture or gross anatomy of the mouse hindlimb and pelvis musculature, but also of use to anyone interested in the functional significance of muscle design in relation to quadrupedal locomotion

A Corpus-Based, Pilot Study of Lexical Stress Variation in American English

Phonological free variation describes the phenomenon of there being more than one pronunciation for a word without any change in meaning (e.g. because, schedule, vehicle). The term also applies to words that exhibit different stress patterns (e.g. academic, resources, comparable) with no change in meaning or grammatical category. A corpus-based analysis of free variation is a useful tool for testing the validity of surveys of speakers' pronunciation preferences for certain variants. The current paper presents the results of a corpus-based pilot study of American English, in an attempt to replicate Mompéan's 2009 study of British English

Causal Classical Theory of Radiation Damping

It is shown how initial conditions can be appropriately defined for the integration of Lorentz-Dirac equations of motion. The integration is performed \QTR{it}{forward} in time. The theory is applied to the case of the motion of an electron in an intense laser pulse, relevant to nonlinear Compton scattering.Comment: 8 pages, 2 figure

EAGLE ISS - A modular twin-channel integral-field near-IR spectrograph

The ISS (Integral-field Spectrograph System) has been designed as part of the EAGLE Phase A Instrument Study for the E-ELT. It consists of two input channels of 1.65x1.65 arcsec field-of-view, each reconfigured spatially by an image-slicing integral-field unit to feed a single near-IR spectrograph using cryogenic volume-phase-holographic (VPH) gratings to disperse the image spectrally. A 4k x 4k array detector array records the dispersed images. The optical design employs anamorphic magnification, image slicing, VPH gratings scanned with a novel cryo-mechanism and a three-lens camera. The mechanical implementation features IFU optics in Zerodur, a modular bench structure and a number of high-precision cryo-mechanisms.Comment: 12 pages, to be published in Proc SPIE 7735: Ground-based & Airborne Instrumentation for Astronomy II

THE EFFECT OF AN EMBARGO OF CALIFORNIA PEACHES

International Relations/Trade,

An experimental study of the temporal statistics of radio signals scattered by rain

A fixed-beam bistatic CW experiment designed to measure the temporal statistics of the volume reflectivity produced by hydrometeors at several selected altitudes, scattering angles, and at two frequencies (3.6 and 7.8 GHz) is described. Surface rain gauge data, local meteorological data, surveillance S-band radar, and great-circle path propagation measurements were also made to describe the general weather and propagation conditions and to distinguish precipitation scatter signals from those caused by ducting and other nonhydrometeor scatter mechanisms. The data analysis procedures were designed to provide an assessment of a one-year sample of data with a time resolution of one minute. The cumulative distributions of the bistatic signals for all of the rainy minutes during this period are presented for the several path geometries

Development of dynamic calibration methods for POGO pressure transducers

Two dynamic pressure sources are described for the calibration of pogo pressure transducers used to measure oscillatory pressures generated in the propulsion system of the space shuttle. Rotation of a mercury-filled tube in a vertical plane at frequencies below 5 Hz generates sinusoidal pressures up to 48 kPa, peak-to-peak; vibrating the same mercury-filled tube sinusoidally in the vertical plane extends the frequency response from 5 Hz to 100 Hz at pressures up to 140 kPa, peak-to-peak. The sinusoidal pressure fluctuations can be generated by both methods in the presence of high pressures (bias) up to 55 MPa. Calibration procedures are given in detail for the use of both sources. The dynamic performance of selected transducers was evaluated using these procedures; the results of these calibrations are presented. Calibrations made with the two sources near 5 Hz agree to within 3% of each other