Individual complex Dirac eigenvalue distributions from random matrix theory and lattice QCD at nonzero chemical potential

We analyze how individual eigenvalues of the QCD Dirac operator at nonzero chemical potential are distributed in the complex plane. Exact and approximate analytical results for such distributions are derived from non-Hermitian random matrix theory. When comparing these to lattice QCD spectra close to the origin, excellent agreement is found for zero and nonzero topology at several values of the chemical potential. Our analytical results are also applicable to other physical systems in the same symmetry class

Distributions of individual Dirac eigenvalues for QCD at non-zero chemical potential: RMT predictions and lattice results

For QCD at non-zero chemical potential $\mu$, the Dirac eigenvalues are scattered in the complex plane. We define a notion of ordering for individual eigenvalues in this case and derive the distributions of individual eigenvalues from random matrix theory (RMT). We distinguish two cases depending on the parameter $\alpha=\mu^2 F^2 V$, where $V$ is the volume and $F$ is the familiar low-energy constant of chiral perturbation theory. For small $\alpha$, we use a Fredholm determinant expansion and observe that already the first few terms give an excellent approximation. For large $\alpha$, all spectral correlations are rotationally invariant, and exact results can be derived. We compare the RMT predictions to lattice data and in both cases find excellent agreement in the topological sectors $\nu=0,1,2$

A Non-Perturbative Treatment of the Pion in the Linear Sigma-Model

Using a non-perturbative method based on the selfconsistent Quasi-particle Random-Phase Approximation (QRPA) we describe the properties of the pion in the linear $\sigma$-model. It is found that the pion is massless in the chiral limit, both at zero- and finite temperature, in accordance with Goldstone's theorem.Comment: To appear in Nucl.Phys. A, 16 pages, 2 Postscript figure

Effective Operators for Double-Beta Decay

We use a solvable model to examine double-beta decay, focusing on the neutrinoless mode. After examining the ways in which the neutrino propagator affects the corresponding matrix element, we address the problem of finite model-space size in shell-model calculations by projecting our exact wave functions onto a smaller subspace. We then test both traditional and more recent prescriptions for constructing effective operators in small model spaces, concluding that the usual treatment of double-beta-decay operators in realistic calculations is unable to fully account for the neglected parts of the model space. We also test the quality of the Quasiparticle Random Phase Approximation and examine a recent proposal within that framework to use two-neutrino decay to fix parameters in the Hamiltonian. The procedure eliminates the dependence of neutrinoless decay on some unfixed parameters and reduces the dependence on model-space size, though it doesn't eliminate the latter completely.Comment: 10 pages, 8 figure

Popularising history: some reflections and experiences.

Paper presented at the Wits History Workshop: The Making of Class, 9-14 February, 1987

Labour and capital saving technical change in telecommunications

The Australian telecommunications sector is being improved and extended through substantial recent investment in intelligent technology such as digital switching, fibre optics, satellite and cellular transmission, and the Internet. These technologies are being progressively integrated with technology from the broadcasting, computer and electronics industries, providing a unified information infrastructure for information transmission and processing. Technological progress embodied in new equipment has the effect of increasing the efficiency of the factors of production. Such efficiency increases can be biased towards a particular factor. For instance, the impact of labour-augmenting technical change is a decline in the cost of labour per unit of production. When such biases are apparent the relativity between the costs of labour and capital per unit of production is changed. In the longer term, technical change can impact on the rate of employment growth and also on the rate of capital accumulation. In this study the Australian telecommunications cost structure is examined for the period 1919 to 1988. To measure labour saving and capital saving technical change a translog cost model is estimated. Multiproduct telecommunications cost studies typically employ the translog cost model (Evans and Heckman, 1984; Roller, 1990a; 1990b; Shin and Ying, 1992; McKenzie and Small, 1997). The translog model places no a priori restrictions on substitution possibilities among the factors of production, and allows scale economies to vary with the level of output.

The cost structure of Australian telecommunications

Since 1991 Australian telecommunications has undergone substantial reform. To a large extent, the economic correctness of pro-competitive policy depends on the non-existence of natural monopoly technology. This paper provides estimates of the Australian telecommunications system cost structure, and tests for subadditivity from 1943 to 1991. Additivity of the cost function after 1945 rejects the natural monopoly hypothesis and supports recent government policy. Diminished natural monopoly characteristics suggest that co-ordination between firms through networking can achieve similar economies as internal co-ordination within a monopoly. This finding is important, given the trend towards network unbundling, and service provision through interconnection.Cost structure of Australian telecommunications