Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

Trial of the Primary Care Practice Improvement Tool: Building organisational performance in Australian general practice and primary health care

Objective: To nationally trial the Primary Care Practice Improvement Tool (PC-PIT), an organisational performance improvement tool previously co-created with Australian primary care practices to increase their focus on relevant quality improvement (QI) activities. Design: The study was conducted from March to December 2015 with volunteer general practices from a range of Australian primary care settings. We used a mixed-methods approach in two parts. Part 1 involved staff in Australian primary care practices assessing how they perceived their practice met (or did not meet) each of the 13 PC-PIT elements of high-performing practices, using a 1–5 Likert scale. In Part 2, two external raters conducted an independent practice visit to independently and objectively assess the subjective practice assessment from Part 1 against objective indicators for the 13 elements, using the same 1–5 Likert scale. Concordance between the raters was determined by comparing their ratings. In-depth interviews conducted during the independent practice visits explored practice managers’ experiences and perceived support and resource needs to undertake organisational improvement in practice. Results: Data were available for 34 general practices participating in Part 1. For Part 2, independent practice visits and the inter-rater comparison were conducted for a purposeful sample of 19 of the 34 practices. Overall concordance between the two raters for each of the assessed elements was excellent. Three practice types across a continuum of higher- to lower-scoring practices were identified, with each using the PC-PIT in a unique way. During the in-depth interviews, practice managers identified benefits of having additional QI tools that relate to the PC-PIT elements. Conclusions: The PC-PIT is an organisational performance tool that is acceptable, valid and relevant to our range of partners and the end users (general practices). Work is continuing with our partners and end users to embed the PC-PIT in existing organisational improvement programs.

Simplified theory of optical nonlinearities in spin-polarized bulk GaAs

Apart from their intrinsic physical interest, spin-polarized many-body effects are expected to be important to the working of spintronic devices. A vast literature exists on the effects of a spin-unpolarized electron-hole plasma on the optical properties of a semiconductor. Here, we include the spin degree of freedom to model optical absorption of circularly polarized light by spin-polarized bulk GaAs. Our model is easy to implement and does not require elaborate numerics, since it is based on the closed-form analytical pair-equation formula that is valid in 3d. The efficacy of our approach is demonstrated by a comparison with recent experimental data.

Non-Fermi liquid theory of quantum hall effects

Within the Grassmannian U(2N)/U(N) x U(N) nonlinear sigma-model representation of localization, one can study the low-energy dynamics of both a free and interacting electron gas. We study the crossover between these two fundamentally different physical problems. We show how the topological arguments for the exact quantization of the Hall conductance are extended to include the Coulomb interaction problem. We discuss dynamical scaling and make contact with the theory of variable range hopping. (C) 2005 Pleiades Publishing, Inc.