Universality Conjecture for all Airy, Sine and Bessel Kernels in the Complex Plane

We address the question of how the celebrated universality of local correlations for the real eigenvalues of Hermitian random matrices of size NxN can be extended to complex eigenvalues in the case of random matrices without symmetry. Depending on the location in the spectrum, particular large-N limits (the so-called weakly non-Hermitian limits) lead to one-parameter deformations of the Airy, sine and Bessel kernels into the complex plane. This makes their universality highly suggestive for all symmetry classes. We compare all the known limiting real kernels and their deformations into the complex plane for all three Dyson indices beta=1,2,4, corresponding to real, complex and quaternion real matrix elements. This includes new results for Airy kernels in the complex plane for beta=1,4. For the Gaussian ensembles of elliptic Ginibre and non-Hermitian Wishart matrices we give all kernels for finite N, built from orthogonal and skew-orthogonal polynomials in the complex plane. Finally we comment on how much is known to date regarding the universality of these kernels in the complex plane, and discuss some open problems.Comment: 16 pages, based on invited talk at MSRI Berkeley, September 201

Nuclear thermionic converter

Efficient nuclear reactor thermionic converter units are described which can be constructed at low cost and assembled in a reactor which requires a minimum of fuel. Each converter unit utilizes an emitter rod with a fluted exterior, several fuel passages located in the bulges that are formed in the rod between the flutes, and a collector receiving passage formed through the center of the rod. An array of rods is closely packed in an interfitting arrangement, with the bulges of the rods received in the recesses formed between the bulges of other rods, thereby closely packing the nuclear fuel. The rods are constructed of a mixture of tungsten and thorium oxide to provide high power output, high efficiency, high strength, and good machinability

The distributional effect of the 2008 Pre-Budget Report

The Pre-Budget Report given by the Chancellor on 24th November 2008 contained a number of changes to the tax and benefit system to come into effect at various points over the next three years. This briefing note expands on the information provided at a briefing given by IFS researchers on the day after the Pre-Budget Report1. It gives details of the changes to taxes, benefits and tax credits directly affecting households, and the total distributional impact of measures announced in PBR 2008 together with pre-announced changes, by income and expenditure decile and household type, at three points in time – January 2009, April 2009 and April 2011. It also discusses what PBR 2008 does to our impression of all tax and benefit changes under this Government. Finally, it discusses what PBR 08 did for child poverty in 2010/11 and the likely effects of the income tax changes for those earning more than £100,000 a year

Why do people live apart together?

Interpretations of living apart together (LAT) have typically counter-posed 'new family form' versus 'continuist' perspectives. Recent surveys, however, construct LAT as a heterogeneous category that supports a 'qualified continuist' position – most people live apart as a response to practical circumstances or as a modern version of 'boy/girlfriend', although a minority represents something new in preferring to live apart more permanently. This article interrogates this conclusion by examining in depth why people live apart together, using a nationally representative survey from Britain and interview accounts from 2011. Our analysis shows that LAT as a category contains different sorts of relationship, with different needs and desires. While overall coupledom remains pivotal and cohabitation remains the goal for most, LAT allows people flexibility and room to manoeuvre in adapting couple intimacy to the demands of contemporary life. Hence, we suggest, LAT is both 'new' and a 'continuation'

Development of field ionization for the improvement of mass spectrometry Interim scientific report, 25 Mar. 1968 - 25 Mar. 1969

Field ionization for improvment of mass spectrometr

Characteristic polynomials in real Ginibre ensembles

We calculate the average of two characteristic polynomials for the real Ginibre ensemble of asymmetric random matrices, and its chiral counterpart. Considered as quadratic forms they determine a skew-symmetric kernel from which all complex eigenvalue correlations can be derived. Our results are obtained in a very simple fashion without going to an eigenvalue representation, and are completely new in the chiral case. They hold for Gaussian ensembles which are partly symmetric, with kernels given in terms of Hermite and Laguerre polynomials respectively, depending on an asymmetry parameter. This allows us to interpolate between the maximally asymmetric real Ginibre and the Gaussian Orthogonal Ensemble, as well as their chiral counterparts

Thermal expansion of the spin-1/2 Heisenberg-chain compound Cu(C4_4H4_4N2_2)(NO3_3)2_2

Compounds containing magnetic subsystems representing simple model spin systems with weak magnetic coupling constants are ideal candidates to test theoretical predictions for the generic behavior close to quantum phase transitions. We present measurements of the thermal expansion and magnetostriction of the spin-1/2-chain compound copper pyrazine dinitrate Cu(C$_4$H$_4$N$_2$)(NO$_3$)$_2$. Of particular interest is the low-temperature thermal expansion close to the saturation field $H_c \simeq 13.9 \mathrm{T}$, which defines a quantum phase transition from the gapless Luttinger liquid state to the fully saturated state with a finite excitation gap. We observe a sign change of the thermal expansion for the different ground states, and at the quantum critical point $H_c$ the low-temperature expansion approaches a $1/\sqrt{T}$ divergence. Thus, our data agree very well with the expected quantum critical behaviour.Comment: 4 pages, 3 figures; to appear in the proceedings of the ICM 09 held in Karlsruhe, German

A comprehensive WebCT integration system

Murdoch University, in collaboration with industry partners, has developed a sophisticated middleware application (WebCTMan) between WebCT and other corporate systems, such as the Callista student records system, the Concept 1 human resources system and Murdoch’s own authentication system. This presentation will describe the architecture and functionality of this system. The impetus for WebCTMan was to enable Murdoch to change its student records database with minimal impact on our WebCT installation. However, WebCTMan now gives us great flexibility in managing our WebCT installation, enabling us to manage courses across teaching periods, and upgrade easily. This paper describes the context in which this system was built and gives an overview of its architecture. Courses in WebCTMan can have a status of active (where student details are updated nightly), inactive (where all students are orphans), and static (where student accounts are valid but not updated). Tools are available to change this status, and easily activate and deactivate courses. Different versions of courses are maintained for each teaching period, resolving the problem of overlap between semesters, when some students still have deferred examinations after the start of a new semester. In addition to managing students, WebCTMan provides functionality to manage staff and courses. Staff can request courses to be created or cloned from other courses. They can also create their own guest accounts and allocate tutors and markers to courses, and download class lists. Operators can create or rename courses on demand, as well as changing the roles of staff, including primary and secondary designers. A subset of functions is available to helpdesk operators, who can lookup details of both students and staff within the system

Random matrix theory of unquenched two-colour QCD with nonzero chemical potential

We solve a random two-matrix model with two real asymmetric matrices whose primary purpose is to describe certain aspects of quantum chromodynamics with two colours and dynamical fermions at nonzero quark chemical potential mu. In this symmetry class the determinant of the Dirac operator is real but not necessarily positive. Despite this sign problem the unquenched matrix model remains completely solvable and provides detailed predictions for the Dirac operator spectrum in two different physical scenarios/limits: (i) the epsilon-regime of chiral perturbation theory at small mu, where mu^2 multiplied by the volume remains fixed in the infinite-volume limit and (ii) the high-density regime where a BCS gap is formed and mu is unscaled. We give explicit examples for the complex, real, and imaginary eigenvalue densities including Nf=2 non-degenerate flavours. Whilst the limit of two degenerate masses has no sign problem and can be tested with standard lattice techniques, we analyse the severity of the sign problem for non-degenerate masses as a function of the mass split and of mu. On the mathematical side our new results include an analytical formula for the spectral density of real Wishart eigenvalues in the limit (i) of weak non-Hermiticity, thus completing the previous solution of the corresponding quenched model of two real asymmetric Wishart matrices.Comment: 45 pages, 31 figures; references added, as published in JHE